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Compound channels play an important role in hydraulic and hydrological engineering. Many rivers and streams have naturally compound channels, which are important for both flood control and river ecosystems. When predicting discharge, interval predictions are usually more realistic and reliable than traditional point predictions made using ML models. In this study, the authors used three well-known machine learning techniques (Adaptive Neuro Fuzzy Inference System (ANFIS), Support Vector Machine (SVM) and Artificial Neural Networks (ANN)) to predict compound channel discharge. To accurately assess uncertainty, two resampling techniques were employed: Bootstrap (B) and Jackknife after Bootstrap (JB). The proposed approach reflects the impacts of statistical uncertainties using prediction confidence intervals and the reliability of point prediction. The JB resampling technique has proven to offer superior accuracy in terms of point prediction and prediction intervals when compared to Bootstrap. Bootstrapping did not yield superior outcomes compared with the standalone ML models. The JB-ANN and JB-ANFIS models outperformed the JB-SVM and Bootstrap ML models in the testing phase, as shown by various statistical measures. This study suggests that the JB-ANN approach is a reliable and robust tool for accurately predicting compound discharges. The findings reveal that when the models have low accuracy in point prediction, the level of uncertainty in predicting the interval also increases. The innovation of this research is enhancing the examination of uncertainties in compound channel discharge by incorporating two resampling techniques to analyze three different ML models. [ABSTRACT FROM AUTHOR]

Missing data reduce the representativeness of the sample and can lead to inference problems. In this article, we apply the Bayesian jackknife empirical likelihood (BJEL) method for inference on data that are missing at random, as well as for causal inference. The semiparametric fractional imputation estimator, propensity score‐weighted estimator, and doubly robust estimator are used for constructing the jackknife pseudo values, which are needed for conducting BJEL‐based inference with missing data. Existing methods, such as normal approximation and JEL, are compared with the BJEL approach in a simulation study. The proposed approach shows better performance in many scenarios in terms of credible intervals. Furthermore, we demonstrate the application of the proposed approach for causal inference problems in a study of risk factors for impaired kidney function. [ABSTRACT FROM AUTHOR]

The duration of extremes in time leads to a phenomenon known as clustering of high values, with a strong impact on risk assessment. The extremal index is a measure developed within Extreme Value Theory that quantifies the degree of clustering of high values. In this work we will consider the cycles estimator introduced in Ferreira and Ferreira (Ann Inst Henri Poincare Probab Stat 54(2):587–605, 2018). A reduced bias estimator based on the Jackknife methodology will be presented. The bootstrap technique will also be considered in the inference and will allow to obtain confidence intervals. The performance will be analyzed based on simulation. We found our proposal effective in reducing bias and it compares favorably with some well-known methods. An application of the methods to real data will also be presented. [ABSTRACT FROM AUTHOR]

Bias correction can often improve the finite sample performance of estimators. We show that the choice of bias correction method has no effect on the higher‐order variance of semiparametrically efficient parametric estimators, so long as the estimate of the bias is asymptotically linear. It is also shown that bootstrap, jackknife, and analytical bias estimates are asymptotically linear for estimators with higher‐order expansions of a standard form. In particular, we find that for a variety of estimators the straightforward bootstrap bias correction gives the same higher‐order variance as more complicated analytical or jackknife bias corrections. In contrast, bias corrections that do not estimate the bias at the parametric rate, such as the split‐sample jackknife, result in larger higher‐order variances in the i.i.d. setting we focus on. For both a cross‐sectional MLE and a panel model with individual fixed effects, we show that the split‐sample jackknife has a higher‐order variance term that is twice as large as that of the "leave‐one‐out" jackknife. [ABSTRACT FROM AUTHOR]

Bayes estimation, multilayer Bayes estimation and E-Bayes estimation of inverse Gaussian distribution parameters are studied respectively under weighted p and q symmetric entropy loss, and the idea of knife cutting method is applied to Bayes estimation. The exact form of Bayes estimation of shape parameter of inverse Gaussian distribution is obtained. R software is used to numerically simulate Bayes estimation, E-Bayes estimation and Jackknife-Bayes estimation of studied parameters by using the random walk Metropolis algorithm. The Bayes estimation precision of the shape parameter of inverse Gaussian distribution under the following loss; weighted p and q symmetric entropy loss, Linex asymmetric loss, square loss and q-symmetric entropy loss is compared, and the results showed that the Bayes estimation of the shape parameter of the inverse Gaussian distribution has higher accuracy under weighted p and q symmetric entropy loss. [ABSTRACT FROM AUTHOR]

When designing confirmatory Phase 3 studies, one usually evaluates one or more efficacious and safe treatment option(s) based on data from previous studies. However, several retrospective research articles reported the phenomenon of "diminished treatment effect in Phase 3" based on many case studies. Even under basic assumptions, it was shown that the commonly used estimator could substantially overestimate the efficacy of selected group(s). As alternatives, we propose a class of computational methods to reduce estimation bias and mean squared error with a broader scope of multiple treatment groups and flexibility to accommodate summary results by group as input. Based on simulation studies and a real data example, we provide practical implementation guidance for this class of methods under different scenarios. For more complicated problems, our framework can serve as a starting point with additional layers built in. Proposed methods can also be widely applied to other selection problems. [ABSTRACT FROM AUTHOR]

Magnolia biondii Pampan., a traditional Chinese medicinal plant, holds significant ornamental and medicinal value. We used the MaxEnt model and ArcGIS software to study the potential habitats of M. biondii in China. The results showed that the model exhibited outstanding accuracy, boasting an average area under the receiver-operator curve (AUC) of 0.955. The distribution of M. biondii was primarily influenced by three key environmental factors: min temperature of coldest month (Bio06), precipitation of warmest quarter (Bio18), and precipitation of coldest quarter (Bio19). Currently, M. biondii habitats are concentrated in East, Central, and Southwest China, covering 107.95 × 104 km2. Notably, Hubei, Henan, and Shandong host the majority of highly suitable areas. Future global warming will have a positive impact on the potential distribution area of M. biondii, and its distribution center has a tendency to migrate to higher latitudes. These findings contribute to the theoretical understanding of plant resources and provide insights into the habitat conservation of M. biondii. [ABSTRACT FROM AUTHOR]

Multicollinearity among independent variables is one of the most common problems in regression models. The aftereffects of this problem, such as ill-conditioning, instability of estimators, and inflating mean squared error of ordinary least squares estimator (OLS), in the multivariate linear regression model (MLRM) are the same that of linear regression models. To combat multicollinearity, several approaches have been presented in the literature. Liu estimator (LE), as a well known estimator in this connection, has been used in linear, generalized linear, and nonlinear regression models by researchers in recent years. In this paper, for the first time, LE and jackknifed Liu estimator (JLE) are investigated in MLRM. To improve estimators in the sense of mean squared error, two known resampling methods, i.e., jackknife and bootstrap, are used. Finally, OLS, LE, and JLE are compared by a simulation study and also using a real data set, by resampling methods in MLRM. [ABSTRACT FROM AUTHOR]

The generalized regression (GREG) estimator is a well-known procedure for using auxiliary data to estimate means or totals using a sample selected from a finite population. The GREG estimator is motivated by an assumed linear superpopulation model and it is known to be asymptotically unbiased regardless of whether the model is correctly specified or not. When the sample size is small and/or when the linear model does not fit the sample data well, the GREG estimator may have nonnegligible bias. In this article, we use the jackknife procedure to correct the bias of the GREG. We evaluate, both theoretically and by simulation, the performance of the jackknife bias-corrected regression estimator (GREG-JK) under unistage sampling without replacement with unequal probabilities. A jackknife mean squared error (MSE) estimator is proposed that naturally includes a finite population correction, which is usually absent in the standard jackknife methods for variance estimation. A simulation study shows that the empirical bias of GREG-JK is negligible for all sample sizes and generated populations. Furthermore, the proposed jackknife MSE estimator demonstrates improvements over the customary estimator. [ABSTRACT FROM AUTHOR]

The area under the Receiver Operating Characteristic (ROC) curve (AUC) is a standard metric for quantifying and comparing binary classifiers. A popular approach to estimating the AUCs and the associated variabilities – the variance of the AUC or the full covariance matrix of multiple correlated AUCs – is the one proposed by DeLong et al. (1988), which is based on the Mann Whitney two-sample U-statistics. The bias of a variance estimator is an important factor in applications such as hypothesis testing and construction of confidence intervals – a negatively biased variance estimator may lead to incorrect conclusions, and a positive bias is conservative hence preferable. In this work, we show that the (co-)variance estimate in DeLong's approach is always positively biased. More specifically, the difference matrix between the expectation of the estimated covariance and the true covariance is a positive semi-definite matrix. This bias is non-negligible when the sample size is small, and quickly diminishes as the sample size increases. Our method relies on constructing, from the AUC kernel, a random variable whose (co-)variance matrix coincides with the bias, thereby establishing the claim. We also discuss alternative approaches to AUC variance estimation that may potentially reduce the bias. • We claim that the bias in DeLong's AUC variance estimation is always non-negative. • We claim that the bias matrix in DeLong's covariance estimation of multiple correlated AUCs is semi-positive definite. • We construct a random variable whose (co-)variance coincides with the bias, thereby establishing the claims. [ABSTRACT FROM AUTHOR]

In this study, we developed a simple technique for effective parameter estimation and prediction of the quantitative structure activity relationship studies using a two‐step procedure. The first step is to choose the important molecular descriptors using the random forest regression, and the second step is to optimally predict the biological activity of the selected chemical compounds using the following estimators: ridge regression, jackknife ridge, Liu regression, jackknife Liu, Kibria–Lukman, and jackknife Kibria–Lukman. We conducted a simulation study and a real‐life analysis with a quantitative structure–activity relationship (QSAR) data with 2540 descriptors after preprocessing. The optimal prediction is determined using the cross‐validation error. The estimator with minimum cross‐validation error is considered best. It is obvious that performing jackknife estimation after random forest selection is preferred. In this study, we developed a simple technique for effective parameter estimation and prediction of the quantitative structure activity relationship studies (QSAR) using a two‐step procedure. We conducted a simulation study and a real‐life application with QSAR data with 2540 descriptors after preprocessing. The optimal prediction is determined using the cross‐validation error. The performance of the methods is judged using the root mean squared error of prediction. It is obvious that performing jackknife estimation after random forest selection is preferred. [ABSTRACT FROM AUTHOR]

Risk assessment is utilized to prioritize preventive measures based on the probability of dispersal success of pests. A main part of the risk assessment procedure is to determine the effects of environmental variables on the current and potential geographical distributions. In the present study, the spatial distribution of the Mediterranean pine engraver, Orthotomicus erosus (Wollaston), was mapped and predicted using MaxEnt. Presence records of O. erosus (north, northeast, west and centre of Iran), environmental and topographic variables, with the lowest correlations among themselves and the highest effects on the pest distribution were used. A total of 76 presence records of O. erosus were collected. The results of the distribution prediction modelling revealed that the northern part of Iran and the areas along the Zagros are the most suitable habitats for this species. Examining environmental variable importance on the distribution of O. erosus showed that the variables related to temperature and precipitation had more contribution in the MaxEnt model, respectively than the altitude. Furthermore, the high accuracy of the model (0.928) indicated that the MaxEnt had an acceptable performance for the prediction of O. erosus distribution. These findings would provide primary and critical information about the potential distribution of O. erosus in Iran, which could be effective for the stable population regulation of this destructive pest.

IntroductionDust is a phenomenon that mainly occurs in arid and semi-arid areas as a result of high wind speed and turbulence on the surface of the soil without vegetation and prone to erosion. Various factors such as wind speed, vegetation cover, soil characteristics, climatic factors, etc. are involved in the creation of wind erosion and the resulting dust, all of which are related to each other and lead to an increase or decrease in wind erosion and dust storms. The problems caused by dust storms are due to the lack of sufficient information about the prevailing conditions in the region, the way these conditions change, and the lack of knowledge of sensitive and prone areas to dust storms. To deal with this phenomenon and provide appropriate management solutions, it is necessary to know the areas prone to dust and the effective factors in the occurrence of this phenomenon. In this regard, remote sensing and modeling can be very effective in investigating the dust phenomenon. Numerous studies have also been conducted to investigate dust storms and dust sources and to model areas sensitive to this phenomenon using remote sensing data and machine learning.Isfahan province is considered one of the most important geographical regions of the country, which is susceptible to successive drought, desertification, and dust storms due to its special geographical location, low rainfall, and proximity to the desert. So, it is necessary to carry out studies that will lead us to a correct understanding of dust-prone areas in this province. Therefore, In the current research, zoning of dust-prone areas in Isfahan province was done using meteorological codes related to dust, Aerosol optical depth values of MODIS sensor of Terra satellite (2001-2022), and machine learning algorithms including RF, BRT, SVM, and CART.Materials and methodsStudy areaIsfahan Province with an area of nearly 107017 km2 (6.4% of Iran area) is located between 30° 43′ to 34° 30′ N and 49° 38′ to 55° 31′ E in central Iran (Fig. 1). The mean annual precipitation of this province is between 40 mm and more than 800 mm and its mean annual temperature varies from 10 °C to 20 °C (Iran Meteorological Organization). According to the Torrent White method, the climate of Isfahan province is dry in 58.73% of its area (eastern, northeastern, and sub-central parts of the province), semi-arid in 28% of its area (central and northern parts of the province), and humid and semi-humid in 13.27% of its area (western and southern parts of the province). MethodologyFirst, using AOD values, the occurrence and non-occurrence points of dust were determined. Ten various factors including land use, temperature, rainfall, erosive wind speed, slope, altitude, albedo, EVI, NDSI, and NDMI were determined as predictive factors. n the next step, the correlation between the predictive factors was calculated using the variance inflation factor (VIF). Using machine learning algorithms, spatial modeling of susceptible areas to dust was done and the importance of predictive factors in zoning was determined using the jackknife test. Finally, using the value of the area under the ROC curve (ROC-AUC), the validation of the model was done.ResultsThe zoning map of dust-prone areas in Isfahan province showed that the low-altitude and flat parts of the north, parts of the northeast, southeast of the province, and the central areas towards the southwest and west of Isfahan province are vulnerable areas against the occurrence of dust.The highest percentage of areas prone to dust in the RF model was in the very low class with a value of 21.36%, in the BRT model was in the medium class with a value of 22.66%, and in the SVM and CART models, it was in very high and low classes with values of 23.92% and 37.6%, respectively. The results of validation illustrated that the RF model with AUC = 0.86 was the most efficient, followed by BRT, CART, and SVM models with AUC values of 0.82, 0.79, and 0.77 respectively. According to the results of the Jackknife test, in RF, BRT, and CART models, rainfall had the most effect in modeling while in the SVM model, temperature and then rainfall had the most effect in the modeling.Discussion and conclusionBased on the results, the most vulnerable areas to dust are assigned to salt land, barren lands, and rangeland with poor quality. These areas, which are mainly located in the northern, central, and parts of the eastern sides of the province, have the lowest amount of surface soil moisture, the lowest amount of rainfall, and the highest temperature, and as a result, they face the lack of vegetation or weak vegetation. Therefore, these areas are exposed to the occurrence of dust, and with winds blowing at a speed exceeding the threshold speed of wind erosion, dust storms will happen. According to the validation results, the RF model has the best performance among the applied models, followed by the BRT, CART, and SVM models. Random forest algorithm is one of the advanced decision tree models used for classification and regression. This algorithm has a much more accurate performance compared to other simple regression trees or parametric statistical methods and is defined based on a large number of decision trees. The results of the jackknife test introduced rainfall as the most important factor in RF, BRT, and CART models. In the RF model, as the best model, after the rainfall factor, the temperature and altitude factors are more important than other factors. Considering the low amount of rainfall in dust-prone areas, it can be said that low rainfall, soil dryness, and, as a result, the reduction of vegetation, increase the conditions for creating wind erosion and dust.

We introduce a new command, summclust, that summarizes the cluster structure of the dataset for linear regression models with clustered disturbances. The key unit of observation for such a model is the cluster. We therefore propose cluster-level measures of leverage, partial leverage, and influence and show how to compute them quickly in most cases. The measures of leverage and partial leverage can be used as diagnostic tools to identify datasets and regression designs in which cluster–robust inference is likely to be challenging. The measures of influence can provide valuable information about how the results depend on the data in the various clusters. We also show how to calculate two jackknife variance matrix estimators efficiently as a by-product of our other computations. These estimators, which are already available in Stata, are generally more conservative than conventional variance matrix estimators. The summclust command computes all the quantities that we discuss. [ABSTRACT FROM AUTHOR]

Two-sample hypothesis testing is a classical problem in statistics. Given i.i.d. samples X1, :::, Xm ~ P and Y1, :::, Yn ~ Q, the two-sample testing is to test whether P is significantly different from Q or not. Among the various statistical tests, the maximum mean discrepancy (MMD) has been proven to have excellent performance compared to traditional methods. In application of MMD, we are confronted with two challenges: (I) For large data set, MMD is computationally demanding with computational cost O((m + n)²); (II) The limiting distribution under the null hypothesis usually contains infinitely many unknown parameters. In this paper, we propose two testing methods that solve (I) and (II) respectively. To address (I), the data are independently and evenly divided into k groups, calculate the MMD on each group and then combine them by empirical likelihood to yield a test statistic Tk: It converges in distribution to the chi-square distribution with degree of freedom one (X1²) under the null hypothesis as k goes to infinity. To address (II), we propose to compute the two-sample jackknife pseudo-values on each group and combine them by empirical likelihood to get a new test statistic Rnm: Under the null hypothesis, Rnm converges in distribution to X1² if k = o(n): The simulation and real data application indicates that the proposed tests performs well. [ABSTRACT FROM AUTHOR]

Risk assessment is utilized to prioritize preventive measures based on the probability of dispersal success of pests. A main part of the risk assessment procedure is to determine the effects of environmental variables on the current and potential geographical distributions. In the present study, the spatial distribution of the Mediterranean pine engraver, Orthotomicus erosus (Wollaston), was mapped and predicted using MaxEnt. Presence records of O. erosus (north, northeast, west and centre of Iran), environmental and topographic variables, with the lowest correlations among themselves and the highest effects on the pest distribution were used. A total of 76 presence records of O. erosus were collected. The results of the distribution prediction modelling revealed that the northern part of Iran and the areas along the Zagros are the most suitable habitats for this species. Examining environmental variable importance on the distribution of O. erosus showed that the variables related to temperature and precipitation had more contribution in the MaxEnt model, respectively than the altitude. Furthermore, the high accuracy of the model (0.928) indicated that the MaxEnt had an acceptable performance for the prediction of O. erosus distribution. These findings would provide primary and critical information about the potential distribution of O. erosus in Iran, which could be effective for the stable population regulation of this destructive pest. [ABSTRACT FROM AUTHOR]

In random-effects models, hierarchical linear models, or multilevel models, it is typically assumed that the variances within higher-level units are homoscedastic, meaning that they are equal across these units. However, this assumption is often violated in research. Depending on the degree of violation, this can lead to biased standard errors of higher-level parameters and thus to incorrect inferences. In this article, we describe a resampling technique for obtaining standard errors—Zitzmann’s jackknife. We conducted a Monte Carlo simulation study to compare the technique with the commonly used delete-1 jackknife, the robust standard error in Mplus, and a modified version of the commonly used delete-1 jackknife. Findings revealed that the resampling techniques clearly outperformed the robust standard error in rather small samples with high levels of heteroscedasticity. Moreover, Zitzmann’s jackknife tended to perform somewhat better than the two versions of the delete-1 jackknife and was much faster.

This paper discusses the problem of the mean changes in time series with heavy-tailed AR(p) noise. Firstly, it proposes a modified ratio-type test statistic, and the results show that under the null hypothesis of no mean change, the asymptotic distribution of the modified statistic is a functional of Lévy processes and the consistency under the alternative hypothesis is obtained. However, a heavy-tailed index exists in the asymptotic distribution and is difficult to estimate. This paper uses bootstrap sampling, jackknife sampling, and subsampling to approximate the distribution under the null hypothesis, and obtain more accurate critical values and empirical power. In addition, some results from a small simulation study and a practical example give an idea of the finite sample behavior of the proposed statistic. [ABSTRACT FROM AUTHOR]

Abstract The assessment of the risk of occurrence of extreme phenomena is inherently linked to the theory of extreme values. In the context of a time series, the analysis of its trajectory toward a greater or lesser smoothness, i.e. presenting a lesser or greater propensity for oscillations, respectively, constitutes another contribution in the assessment of the risk associated with extreme observations. For example, a financial market index with successive oscillations between high and low values shows investors a more unstable and uncertain behavior. In stationary time series, the upper tail smoothness coefficient is described by the tail dependence coefficient, a well-known concept first introduced by Sibuya. This work focuses on an inferential analysis of the upper tail smoothness coefficient, based on subsampling techniques for time series. In particular, we propose an estimator with reduced bias. We also analyze the estimation of confidence intervals through a block bootstrap methodology and a test procedure to prior detect the presence or absence of smoothness. An application to real data is also presented. [ABSTRACT FROM AUTHOR]

In random-effects models, hierarchical linear models, or multilevel models, it is typically assumed that the variances within higher-level units are homoscedastic, meaning that they are equal across these units. However, this assumption is often violated in research. Depending on the degree of violation, this can lead to biased standard errors of higher-level parameters and thus to incorrect inferences. In this article, we describe a resampling technique for obtaining standard errors—Zitzmann's jackknife. We conducted a Monte Carlo simulation study to compare the technique with the commonly used delete-1 jackknife, the robust standard error in Mplus, and a modified version of the commonly used delete-1 jackknife. Findings revealed that the resampling techniques clearly outperformed the robust standard error in rather small samples with high levels of heteroscedasticity. Moreover, Zitzmann's jackknife tended to perform somewhat better than the two versions of the delete-1 jackknife and was much faster. [ABSTRACT FROM AUTHOR]

Climate change impacts on tropical forests and tree species have been documented as changes in distribution, growing period, phenology, habitat, productivity, species composition, and migration. This study attempts to assess the current and future habitat suitability distribution of two dominant species of Central India, teak (Tectona grandis Linn. f.) and sal (Shorea robusta Gaertn. f.) using a maximum entropy (MaxEnt) model to predict species occurrences by finding the distribution that has the most spread. The future suitable habitat ranges of the species were modeled for two time periods (2050 and 2070) and two representative concentration pathways (RCP 2.6 and 8.5). Representative concentration pathways are scenarios that describe alternative trajectories for carbon dioxide emissions and the resulting atmospheric concentration from 2000 to 2100. We collected and modeled the spatially well-dispersed species occurrence points of teak and sal. The results suggested an increase in suitable habitat range for teak and a decrease for sal for both time periods and RCPs. Furthermore, the jackknife analysis identified temperature and precipitation seasonality as the major variables that influence the distribution of teak. In the case of sal, minimum temperature makes the maximum contribution to distribution changes. The suitable silvicultural strategies for forest management are proposed based on the future distribution of species in relation to the climate variables responsible for the change in their distribution range. These findings and strategies will help forest departments build future management plans for teak and sal forest with a focus on minimizing the impact of climate change. Study Implications: Our study used maximum entropy (MaxEnt) modeling to understand the impact of changing climate on the distribution of teak and sal forests of central India and to propose future silvicultural strategies. The study used MaxEnt model for two time periods and two climate change scenarios at highest resolution. An increase in future suitable habitat for teak and a decrease for sal is predicted by the model. Temperature for teak and precipitation for sal were identified as the major influencing climatic variables. We recommend forest and other related government departments to commission focused research to understand the changing patterns of species with climate change and design appropriate silviculture strategies for effective management. [ABSTRACT FROM AUTHOR]

In this paper, we propose robust meta‐analysis procedures for individual studies that report a broad range of robust summary statistics for a two‐sample problem. Summary statistics of individual studies could be presented in different forms including full data, medians of the two samples, the Hodges‐Lehman and Wilcoxon estimates of the location shift parameters. Data synthesis is made under both fixed‐effect and random‐effect meta‐analysis models. We systematically compare these robust meta‐analysis procedures via simulation studies to meta‐analysis procedure based on sample means and variances from individual studies under a wide range of error distributions. We show that the coverage probabilities of the robust meta‐analysis confidence intervals are quite close to the nominal confidence level. We also show that mean square error (MSE) of the robust meta‐analysis estimator is considerably smaller than that of the non‐robust meta‐analysis estimator under the contaminated normal, heavy tailed and skewed error distributions. The robust meta‐analysis procedures are then applied to platelet count reduction for malaria infected patients in Ghana. [ABSTRACT FROM AUTHOR]

This article studies the asymptotic properties of and alternative inference methods for kernel density estimation (KDE) for dyadic data. We first establish uniform convergence rates for dyadic KDE. Second, we propose a modified jackknife empirical likelihood procedure for inference. The proposed test statistic is asymptotically pivotal regardless of presence of dyadic clustering. The results are further extended to cover the practically relevant case of incomplete dyadic data. Simulations show that this modified jackknife empirical likelihood-based inference procedure delivers precise coverage probabilities even with modest sample sizes and with incomplete dyadic data. Finally, we illustrate the method by studying airport congestion in the United States. [ABSTRACT FROM AUTHOR]

Modern statistical analysis often involves large data sets, for which conventional estimation methods are not suitable, owing to limited computational resources. To solve this problem, we propose a novel subsampling-based method with jackknifing. The key idea is to treat the whole sample as if it were the population. Then, we obtain multiple subsamples with greatly reduced sizes using simple random sampling with replacement. We do not recommend sampling methods without replacement, because this would incur a significant data processing cost when the processing occurs on a hard drive. However, such a cost does not exist if the data are processed in memory. Because subsampled data have relatively small sizes, they can be comfortably read into computer memory and processed. Based on subsampled data sets, jackknife-debiased estimators can be obtained for the target parameter. The resulting estimators are statistically consistent, with an extremely small bias. Finally, the jackknife-debiased estimators from different subsamples are averaged to form the final estimator. We show theoretically that the final estimator is consistent and asymptotically normal. Furthermore, its asymptotic statistical efficiency can be as good as that of the whole sample estimator under very mild conditions. The proposed method is easily implemented on most computer systems, and thus is widely applicable. [ABSTRACT FROM AUTHOR]

Linking errors in item response models quantify the dependence on the chosen items in means, standard deviations, or other distribution parameters. The jackknife approach is frequently employed in the computation of the linking error. However, this jackknife linking error could be computationally tedious if many items were involved. In this article, we provide an analytical approximation of the jackknife linking error. The newly proposed approach turns out to be computationally much less demanding. Moreover, the new linking error approach performed satisfactorily for datasets with at least 20 items.

Regression analyses of how state occupation probabilities or expected lengths of stay depend on covariates in multistate settings can be performed using the pseudo-observation method, which involves calculating jackknife pseudo-observations based on some estimator of the expected value of the outcome. In this article, we present a new command, stpmstate, that calculates such pseudo-observations based on the Aalen–Johansen estimator. We give examples of use of the command, and we conduct a small simulation study to offer insights into the pseudo-observation regression approach. [ABSTRACT FROM AUTHOR]

Statistical agencies are often asked to produce small area estimates (SAEs) for positively skewed variables. When domain sample sizes are too small to support direct estimators, effects of skewness of the response variable can be large. As such, it is important to appropriately account for the distribution of the response variable given available auxiliary information. Motivated by this issue and in order to stabilize the skewness and achieve normality in the response variable, we propose an area-level log-measurement error model on the response variable. Then, under our proposed modeling framework, we derive an empirical Bayes (EB) predictor of positive small area quantities subject to the covariates containing measurement error. We propose a corresponding mean squared prediction error (MSPE) of EB predictor using both a jackknife and a bootstrap method. We show that the order of the bias is O (m − 1) , where m is the number of small areas. Finally, we investigate the performance of our methodology using both design-based and model-based simulation studies. [ABSTRACT FROM AUTHOR]

In the context of right‐censored and interval‐censored data, we develop asymptotic formulas to compute pseudo‐observations for the survival function and the restricted mean survival time (RMST). These formulas are based on the original estimators and do not involve computation of the jackknife estimators. For right‐censored data, Von Mises expansions of the Kaplan–Meier estimator are used to derive the pseudo‐observations. For interval‐censored data, a general class of parametric models for the survival function is studied. An asymptotic representation of the pseudo‐observations is derived involving the Hessian matrix and the score vector. Theoretical results that justify the use of pseudo‐observations in regression are also derived. The formula is illustrated on the piecewise‐constant‐hazard model for the RMST. The proposed approximations are extremely accurate, even for small sample sizes, as illustrated by Monte Carlo simulations and real data. We also study the gain in terms of computation time, as compared to the original jackknife method, which can be substantial for a large dataset. [ABSTRACT FROM AUTHOR]

Abstract Background Precision medicine is an emerging field that involves the selection of treatments based on patients’ individual prognostic data. It is formalized through the identification of individualized treatment rules (ITRs) that maximize a clinical outcome. When the type of outcome is time-to-event, the correct handling of censoring is crucial for estimating reliable optimal ITRs. Methods We propose a jackknife estimator of the value function to allow for right-censored data for a binary treatment. The jackknife estimator or leave-one-out-cross-validation approach can be used to estimate the value function and select optimal ITRs using existing machine learning methods. We address the issue of censoring in survival data by introducing an inverse probability of censoring weighted (IPCW) adjustment in the expression of the jackknife estimator of the value function. In this paper, we estimate the optimal ITR by using random survival forest (RSF) and Cox proportional hazards model (COX). We use a Z-test to compare the optimal ITRs learned by RSF and COX with the zero-order model (or one-size-fits-all). Through simulation studies, we investigate the asymptotic properties and the performance of our proposed estimator under different censoring rates. We illustrate our proposed method on a phase III clinical trial of non-small cell lung cancer data. Results Our simulations show that COX outperforms RSF for small sample sizes. As sample sizes increase, the performance of RSF improves, in particular when the expected log failure time is not linear in the covariates. The estimator is fairly normally distributed across different combinations of simulation scenarios and censoring rates. When applied to a non-small-cell lung cancer data set, our method determines the zero-order model (ZOM) as the best performing model. This finding highlights the possibility that tailoring may not be needed for this cancer data set. Conclusion The jackknife approach for estimating the value function in the presence of right-censored data shows satisfactory performance when there is small to moderate censoring. Winsorizing the upper and lower percentiles of the estimated survival weights for computing the IPCWs stabilizes the estimator.

Linking errors in item response models quantify the dependence on the chosen items in means, standard deviations, or other distribution parameters. The jackknife approach is frequently employed in the computation of the linking error. However, this jackknife linking error could be computationally tedious if many items were involved. In this article, we provide an analytical approximation of the jackknife linking error. The newly proposed approach turns out to be computationally much less demanding. Moreover, the new linking error approach performed satisfactorily for datasets with at least 20 items. [ABSTRACT FROM AUTHOR]

In this study, we provide Theil-Sen parameter estimators, which are in multiple linear regression model based on a spatial median, to be examined by the jackknife method. To obtain the proposed estimator, apply the jackknife to a multivariate Theil-Sen estimator (MTSE) from Dang et al. estimators, who proved that the MTSE estimator is asymptotically normal. Robustness, efficiency, and non-normality of the proposed estimator is tested with simulation studies. As a result, the proposed estimator is shown to be robust, consistent, and more efficient in multiple linear regression models with arbitrary error distributions. Also, it is seen that the proposed estimator reduces the effects of outliers even more and gives more reliable results. So, it is clearly observed that the proposed estimator improves the outcome of the multivariate Theil-Sen estimator. In addition, we support with the aid of numerical examples to these results.

In mixture with varying concentrations model (MVC) one deals with a nonhomogeneous sample which consists of subjects belonging to a fixed number of different populations (mixture components). The population which a subject belongs to is unknown, but the probabilities to belong to a given component are known and vary from observation to observation. The distribution of subjects’ observed features depends on the component which it belongs to. Generalized estimating equations (GEE) for Euclidean parameters in MVC models are considered. Under suitable assumptions the obtained estimators are asymptotically normal. A jackknife (JK) technique for the estimation of their asymptotic covariance matrices is described. Consistency of JK-estimators is demonstrated. An application to a model of mixture of nonlinear regressions and a real life example are presented.

Background: Precision medicine is an emerging field that involves the selection of treatments based on patients' individual prognostic data. It is formalized through the identification of individualized treatment rules (ITRs) that maximize a clinical outcome. When the type of outcome is time-to-event, the correct handling of censoring is crucial for estimating reliable optimal ITRs. Methods: We propose a jackknife estimator of the value function to allow for right-censored data for a binary treatment. The jackknife estimator or leave-one-out-cross-validation approach can be used to estimate the value function and select optimal ITRs using existing machine learning methods. We address the issue of censoring in survival data by introducing an inverse probability of censoring weighted (IPCW) adjustment in the expression of the jackknife estimator of the value function. In this paper, we estimate the optimal ITR by using random survival forest (RSF) and Cox proportional hazards model (COX). We use a Z-test to compare the optimal ITRs learned by RSF and COX with the zero-order model (or one-size-fits-all). Through simulation studies, we investigate the asymptotic properties and the performance of our proposed estimator under different censoring rates. We illustrate our proposed method on a phase III clinical trial of non-small cell lung cancer data. Results: Our simulations show that COX outperforms RSF for small sample sizes. As sample sizes increase, the performance of RSF improves, in particular when the expected log failure time is not linear in the covariates. The estimator is fairly normally distributed across different combinations of simulation scenarios and censoring rates. When applied to a non-small-cell lung cancer data set, our method determines the zero-order model (ZOM) as the best performing model. This finding highlights the possibility that tailoring may not be needed for this cancer data set. Conclusion: The jackknife approach for estimating the value function in the presence of right-censored data shows satisfactory performance when there is small to moderate censoring. Winsorizing the upper and lower percentiles of the estimated survival weights for computing the IPCWs stabilizes the estimator. [ABSTRACT FROM AUTHOR]

Summary: In recent years, small area estimation has played an important role in statistics as it deals with the problem of obtaining reliable estimates for parameters of interest in areas with small or even zero sample sizes corresponding to population sizes. Nested error linear regression models are often used in small area estimation assuming that the covariates are measured without error and also the relationship between covariates and response variable is linear. Small area models have also been extended to the case in which a linear relationship may not hold, using penalised spline (P‐spline) regression, but assuming that the covariates are measured without error. Recently, a nested error regression model using a P‐spline regression model, for the fixed part of the model, has been studied assuming the presence of measurement error in covariate, in the Bayesian framework. In this paper, we propose a frequentist approach to study a semi‐parametric nested error regression model using P‐splines with a covariate measured with error. In particular, the pseudo‐empirical best predictors of small area means and their corresponding mean squared prediction error estimates are studied. Performance of the proposed approach is evaluated through a simulation and also by a real data application. We propose a frequentist approach to study a semi‐parametric nested error regression model using P‐splines with a covariate measured with error. [ABSTRACT FROM AUTHOR]

In statistical modeling, partial least squares (PLS) regression is one of the most popular techniques for prediction problems. An important but often overlooked problem is that the estimation of prediction confidence intervals always contains an unobserved response value with a specified probability. Therefore, in the present work, we studied how to estimate prediction intervals in PLS regression without any distributional assumptions on data. First, a recently proposed method, jackknife+, is introduced to PLS regression for uncertainty quantification. Second, a novel approach is developed to construct distribution‐free prediction intervals. Finally, empirical studies on simulations and three real‐world datasets show that the proposed method has better coverage properties than other state‐of‐the‐art methods. In this paper, the idea of distribution‐free predictive inference is introduced to chemometrics. Some relevant distribution‐free predictive inference methods, such as jackknife+, cross‐validation+ (CV+), and jackknife+‐after‐bootstrap, are introduced and applied to analyze real‐world molecular descriptor datasets. A novel distribution‐free predictive inference method named leave‐one‐bag‐out+ (LOBO+) is proposed. LOBO+ shows better performance than state‐of‐the‐art methods on simulation and real‐word molecular descriptor datasets. [ABSTRACT FROM AUTHOR]

In mixture with varying concentrations model (MVC) one deals with a nonhomogeneous sample which consists of subjects belonging to a fixed number of different populations (mixture components). The population which a subject belongs to is unknown, but the probabilities to belong to a given component are known and vary from observation to observation. The distribution of subjects' observed features depends on the component which it belongs to. Generalized estimating equations (GEE) for Euclidean parameters in MVC models are considered. Under suitable assumptions the obtained estimators are asymptotically normal. A jackknife (JK) technique for the estimation of their asymptotic covariance matrices is described. Consistency of JK-estimators is demonstrated. An application to a model of mixture of nonlinear regressions and a real life example are presented. [ABSTRACT FROM AUTHOR]

Narrow-ranging species are usually omitted from Species distribution models (SDMs) due to statistical constraints, while they are predicted to be particularly vulnerable to climate change. The recently available high-resolution environmental predictors, along with recently developed methods enable to increase the eligibility of narrow-ranging species for SDMs, provided their distribution is well known. We fill a gap of knowledge on the effect of predicted climate change on narrow-ranging species. We modelled the distribution of the golden mantella frog Mantella aurantiaca and the Manapany day gecko Phelsuma inexpectata, for which the distribution of their occurrence records is well documented. Our modelling scheme included a range of processes susceptible to address statistical issues related to narrow-ranging species. We predict an alarming decline in climate suitability in the whole current distribution area of both species by 2070, potentially leading to a complete extinction in most scenarios. We identified the areas with the best climate suitability in the future, but these remain largely suboptimal regarding species climatic niche. The high level of habitat fragmentation suggests that both species likely need to be at least partly translocated. Climate change may not only drive range contractions or distribution shifts in narrow-ranging species, but may lead to the complete extirpation of suitable environments across their entire region. This study suggests that the level of threats of narrow-ranging species already identified as threatened may be underestimated, especially in heterogeneous tropical areas. We stress the need to develop sampling campaigns and implement proactive actions for narrow-ranging species in the tropics.

This paper discusses the problem of the mean changes in time series with heavy-tailed AR(p) noise. Firstly, it proposes a modified ratio-type test statistic, and the results show that under the null hypothesis of no mean change, the asymptotic distribution of the modified statistic is a functional of Lévy processes and the consistency under the alternative hypothesis is obtained. However, a heavy-tailed index exists in the asymptotic distribution and is difficult to estimate. This paper uses bootstrap sampling, jackknife sampling, and subsampling to approximate the distribution under the null hypothesis, and obtain more accurate critical values and empirical power. In addition, some results from a small simulation study and a practical example give an idea of the finite sample behavior of the proposed statistic.

Structural Equation Models (SEMs) are typically estimated via Maximum Likelihood. Grounded in large sample theory, estimates are prone to finite sample bias. Although Restricted Maximum Likelihood (REML) can alleviate this bias, its applicability is constrained to SEMs that are mathematically equivalent to mixed effect models. Via Monte Carlo simulations, we explored whether resampling based corrections could serve as viable, more broadly applicable alternatives. Results indicate that Bootstrap and Jackknife corrections effectively attenuate small sample bias, at the expected expense of an increase in variability. Similar conclusions are drawn with respect to a more recently proposed analytic approach by Ozenne et al., which was included for comparison. For all corrective methods, caution is advised when dealing with non-normal data and/or low reliability. [ABSTRACT FROM AUTHOR]

Abstract The COVID-19 death predictions are helpful for the formulation of public policies, allowing the use of more effective social isolation strategies with less economic and social impact. This article evaluates a wide range of forecasting methods to identify the best models for predicting cumulative and daily deaths caused by COVID-19 in Brazil, considering a forecast for a seven-day horizon. With the seven-day horizon, the predictions have more accuracy. The dataset is from Oxford Covid-19 Government Response Tracker. The jackknife resampling technique was implemented, thus providing an accurate estimate for evaluating the predictive capacity of the models. Each model was fitted with 266 jackknife samples considering 30-day training bases. The comparison between predictions was made using the average results, considering R2, MAPE, RMSE, and MAE. Models from different classes were adopted: 1 ETS, 4 ARIMA, 18 regression models, and 7 machine learning algorithms. The cumulative death models produce better results than daily deaths, as the cumulative death models are less influenced by time series components: cycle and seasonality. The best results for predicting daily deaths were attained by the Ridge regression method. The best results for predicting cumulative deaths were obtained by the Cubist regression method.

Principal component analysis continues to be a powerful tool for the dimension reduction of high-dimensional data. We assume a variance-diverging model and use the high-dimension low-sample-size asymptotics to show that even though the principal component directions are not consistent, the sample and prediction principal component scores can be useful in revealing the population structure. We further show that these scores are biased, and that the bias is asymptotically decomposed into rotation and scaling parts. We propose bias-adjustment methods that are shown to be consistent and work well in high-dimensional situations with small sample sizes. The potential advantage of the bias adjustment is demonstrated in a classification setting. [ABSTRACT FROM AUTHOR]

In this article I recommend a better point estimator for Krippendorff's Alpha agreement coefficient, and develop a jackknife variance estimator that leads to much better interval estimation than does the customary bootstrap procedure or an alternative bootstrap procedure. Having developed the new methodology, I analyze nominal data previously analyzed by Krippendorff, and two experimentally observed datasets: (1) ordinal data from an imaging study of congenital diaphragmatic hernia, and (2) United States Environmental Protection Agency air pollution data for the Philadelphia, Pennsylvania area. The latter two applications are novel. The proposed methodology is now supported in version 2.0 of my open source R package, krippendorffsalpha, which supports common and user-defined distance functions, and can accommodate any number of units, any number of coders, and missingness. Interval computation can be parallelized. [ABSTRACT FROM AUTHOR]

Para la fiabilidad de sistemas uno de los objetivos principales es estimar la función de confiabilidad usando los estimadores de Kaplan-Meier y Nelson-Aalen, bajo el enfoque no paramétrico. Cuando se recurren a técnicas computacionales, la estrategia de Jackknife delete-I brinda ventajas por sus propiedades de consistencia para la estimación de la varianza. Sin embargo, se tiene incertidumbre sobre la posibilidad de mejorar las estimaciones cuando se aumenta el número (d) de observaciones que son suprimidas en el procedimiento secuencial de Jackknife delete-d. Por otra parte, por sus propiedades asintóticas de estabilización de la varianza, las trans- formaciones log y log(-log) son usadas para encontrar intervalos de confianza (ic) para la función de confiabilidad. En este trabajo, se propone combinar simultáneamente las dos estrategias para encontrar los ic para la función de confiabilidad, proponiendo un nuevo procedimiento que no requiere de ajuste paramétrico en el tiempo de ocurrencia del evento de interés. Además de mejorar la estimación de la función de confiabilidad cuando los porcentajes de censura son altos y los tamaños de muestra pequeños. En la investigación se realiza una comparación vía simulación con tamaños de muestras (10,25,50) y porcentajes de datos censurados (0%,15%,50%) para calcular las tasas de error (T.E) e índices de calidad (I), mejorando las estimaciones con porcentajes de censura altos (50%). Los resultados de este trabajo muestran que se puede mejorar la estimación por intervalo en escenarios complejos de censuras y tamaños de muestra a la literatura del análisis de datos en confiabilidad.

The Canonical Polyadic (CP) tensor decomposition is frequently used as a model in applications in a variety of different fields. Using jackknife resampling to estimate parameter uncertainties is often desirable but results in an increase of the already high computational cost. Upon observation that the resampled tensors, though different, are nearly identical, we show that it is possible to extend the recently proposed Concurrent ALS (CALS) technique to a jackknife resampling scenario. This extension gives access to the computational efficiency advantage of CALS for the price of a modest increase (typically a few percent) in the number of floating point operations. Numerical experiments on both synthetic and real-world datasets demonstrate that the new workflow based on a CALS extension can be several times faster than a straightforward workflow where the jackknife submodels are processed individually.