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The beta regression model is a flexible model, which widely used when the dependent variable is in ratios and percentages in the range of (0.1). The coefficients of the beta regression model are estimated using the maximum likelihood method. In cases where there is a multicollinearity problem, the use of maximum likelihood (ML) leads to problems such as inconsistent parameter estimates and inflated variance.In the presence of multicollinearity, the use of maximum likelihood (ML) leads to problems such as inconsistent parameter estimates and inflated variance. In this study, KL estimator and its jackknifed version are proposed to reduce the effects of multicollinearity in the beta regression model. The performance of the proposed jackknifed KL beta regression estimator is compared with ridge, Liu and KL estimators through simulation studies and real data applications. The results show that the proposed estimators mostly outperform ML, ridge, Liu and KL estimators. [ABSTRACT FROM AUTHOR]

Summary Societal Impact Statement Summary Novel phylogenetic approaches have emerged in recent years to study traditional medicinal plants, aiming to identify potential sources of new drugs. This line of research holds considerable promise yet remains in its early stages. Here, we examine the prevalent methods employed in the field, revealing the impact of methodological choices that have often been made arbitrarily. We also highlight a widespread misconception regarding ‘hot node analysis’, a tool gaining popularity for identifying plants with high bioactive potential. Our findings should advance future research aimed at guiding the selection of promising candidates for bioprospection. Advances in phylogenetics offer a ground‐breaking approach to analysing ethnobotanical data. This line of research typically involves calculating the degree of phylogenetic clustering (i.e. phylogenetic divergence) of a set of medicinal plants and identifying clades with a significant overabundance of these plants, known as hot nodes, which are purportedly responsible for the clustering patterns. However, despite showing great promise, the adequacy of this procedure remains to be tested, and the results have so far been inconclusive and, at times, contradictory. Here, we examine two key elements through a case study of Ecuadorian medicinal flora: the impact of taxonomic resolution (species‐ and genus‐level data) on phylogenetic divergence metrics (Mean Pairwise Distance; MPD, and Mean Nearest Taxon Distance; MNTD), and the efficacy of the hot node analysis in identifying clades that significantly influence these metrics. To identify clades with a significant impact on MPD and MNTD, we implemented a jackknifing procedure and compared outcomes with the hot nodes. Phylogenetic divergence was strongly dependent on the taxonomic resolution, with clustering mainly revealed by MPD at the genus level. Further, the hot nodes incompletely matched those with significant influence on MPD and MNTD according to the jackknifing analysis. We highlight the impact of taxonomic resolution on commonly used phylogenetic divergence metrics and the limitations of hot nodes in identifying influential clades, stressing the potential of alternative jackknifing techniques. We recommend the use of the most resolved tree possible and combining jackknifing with hot node analyses as complementary sources to pinpoint clades for bioprospection. [ABSTRACT FROM AUTHOR]

The electrification of towing and trailing units creates new torque allocation alternatives among different units of articulated heavy vehicles. To increase the power and energy efficiency, control algorithms can request propulsion or regenerative braking from a single unit while keeping the other units unbraked or unpropelled. However, this may lead to safety problems, such as jackknifing or trailer swing. This paper uses a high-fidelity simulation tool to formulate safe operating envelopes for a tractor and semitrailer combination for braking-in-turn cases. The effects of different vehicle and environment parameters on the safe operating envelope are studied. The safe operating envelope obtained is then validated using real vehicle tests and can be used with any control algorithm to avoid requesting unsafe unit force combinations. [ABSTRACT FROM AUTHOR]

In the past two decades, model averaging has attracted more and more attention and is regarded as a much better tool to solve model uncertainty than model selection. Compared with the conditional mean regression, the quantile regression serves as a robust alternative and shows a lot more information about the conditional distribution of a response variable. In this paper, we propose a jackknife model averaging procedure that chooses the weights by minimizing a leave-one-out cross-validation criterion function for mixed-data kernel-weighted spline quantile regressions that contain both continuous and categorical regressors when all candidate models are potentially misspecified. We demonstrate the JMA estimator is asymptotically optimal in terms of minimizing the out-of-sample final prediction error. Simulation experiments are conducted to assess the relative finite-sample performance of the proposed JMA method with respect to other model selection and averaging methods. Our JMA method is applied to the wage and house datasets. [ABSTRACT FROM AUTHOR]

In the past 20 years, model averaging has been developed as a better tool than model selection in statistical prediction. Expectile prediction is widely used for modeling data with the heterogeneous conditional distribution. In this article, we introduce a model averaging estimator for additive expectile prediction. The resulting model averaging estimator is shown to have asymptotic optimality under some regular conditions. Simulation experiments are conducted to demonstrate that the performance of our method is better than that of other common model selection and model averaging methods under the finite-sample case. Our method is also verified in the house and wage datasets. [ABSTRACT FROM AUTHOR]

Articulated heavy vehicles exhibit poor lateral stability, which may lead to unstable motion modes, e.g., trailer-sway and jackknifing, causing severe accidents. Varying relevant vehicle parameters improves the static stability but degrades the dynamic stability. The past studies focused either on the static or dynamic stability alone. However, little attention has been paid to exploring the trade-off between the static and dynamic stabilities. To gain design insights for active safety systems for AHVs, this article studies this trade-off systematically. To this end, a systematic method is proposed to conduct the linear stability and trade-off analysis. To implement and demonstrate the proposed method, a linear three-degrees-of-freedom yaw-plane model is generated to represent a tractor/semi-trailer. A trade-off analysis is conducted considering two tractor rear-axle configurations and three trailer payload arrangements. In each case, simulation is performed in both steady-state and transient testing maneuvers. To validate the linear stability analysis based on the linear yaw-plane model, two nonlinear TruckSim models are introduced, and the corresponding simulation is conducted. Insightful understanding of the trade-off is gained through analyzing the simulation results, and the linear stability analysis will provide valuable guidelines for the design and development of active safety systems for AHVs. [ABSTRACT FROM AUTHOR]

Bioenergetics models are powerful tools used to address a range of questions in fish biology. However, these models are rarely informed by free‐swimming activity data, introducing error. To quantify the costs of activity in free‐swimming fish, calibrations produced from standardized laboratory trials can be applied to estimate energy expenditure from sensor data for specific tags and species. Using swim tunnel respirometry, we calibrated acceleration sensor‐equipped transmitting tags to estimate the aerobic metabolic rates (ṀO2) of lake trout (Salvelinus namaycush) at three environmentally relevant temperatures. Aerobic and swim performance were also assessed. Like other calibrations, we found strong relationships between ṀO2 and acceleration or swimming speed, and jackknife validations and data simulations suggest that our models accurately predict metabolic costs of activity in adult lake trout (~5% algebraic error and ~20% absolute error). Aerobic and swim performance metrics were similar to those reported in other studies, but their critical swimming speed was lower than expected. Additionally, lake trout exhibited a wide aerobic scope, suggesting that the avoidance of waters ≥15°C may be related to selection for optimal growing temperatures. The ability to quantify the free‐swimming energetic costs of activity will advance our understanding of lake trout ecology and may yield improvements to bioenergetics model. [ABSTRACT FROM AUTHOR]

Linear mixed models are commonly used in analyzing stepped-wedge cluster randomized trials. A key consideration for analyzing a stepped-wedge cluster randomized trial is accounting for the potentially complex correlation structure, which can be achieved by specifying random-effects. The simplest random effects structure is random intercept but more complex structures such as random cluster-by-period, discrete-time decay, and more recently, the random intervention structure, have been proposed. Specifying appropriate random effects in practice can be challenging: assuming more complex correlation structures may be reasonable but they are vulnerable to computational challenges. To circumvent these challenges, robust variance estimators may be applied to linear mixed models to provide consistent estimators of standard errors of fixed effect parameters in the presence of random-effects misspecification. However, there has been no empirical investigation of robust variance estimators for stepped-wedge cluster randomized trials. In this article, we review six robust variance estimators (both standard and small-sample bias-corrected robust variance estimators) that are available for linear mixed models in R, and then describe a comprehensive simulation study to examine the performance of these robust variance estimators for stepped-wedge cluster randomized trials with a continuous outcome under different data generators. For each data generator, we investigate whether the use of a robust variance estimator with either the random intercept model or the random cluster-by-period model is sufficient to provide valid statistical inference for fixed effect parameters, when these working models are subject to random-effect misspecification. Our results indicate that the random intercept and random cluster-by-period models with robust variance estimators performed adequately. The CR3 robust variance estimator (approximate jackknife) estimator, coupled with the number of clusters minus two degrees of freedom correction, consistently gave the best coverage results, but could be slightly conservative when the number of clusters was below 16. We summarize the implications of our results for the linear mixed model analysis of stepped-wedge cluster randomized trials and offer some practical recommendations on the choice of the analytic model. [ABSTRACT FROM AUTHOR]

County level estimates of mean sheet and rill erosion from the Conservation Effects Assessment Project (CEAP) are useful for program development and evaluation. Since county sample sizes in the CEAP survey are insufficient to support reliable direct estimators, small area estimation procedures are needed. The quantity of water runoff is a useful covariate but is unavailable for the full population. We use an estimate of mean runoff from the CEAP survey as a covariate in a small area model with sheet and rill erosion as the response. As the runoff and sheet and rill erosion are estimators from the same survey, the measurement error in the covariate is important as is the correlation between the measurement error and the sampling error. We conduct a detailed investigation of small area estimation in the presence of a correlation between the measurement error in the covariate and the sampling error in the response. In simulations, the proposed predictor is superior to small area predictors that assume the response and covariate are uncorrelated or that ignore the measurement error entirely. [ABSTRACT FROM AUTHOR]

In clinical trials of longitudinal continuous outcomes, reference based imputation (RBI) has commonly been applied to handle missing outcome data in settings where the estimand incorporates the effects of intercurrent events, e.g. treatment discontinuation. RBI was originally developed in the multiple imputation framework, however recently conditional mean imputation (CMI) combined with the jackknife estimator of the standard error was proposed as a way to obtain deterministic treatment effect estimates and correct frequentist inference. For both multiple and CMI, a mixed model for repeated measures (MMRM) is often used for the imputation model, but this can be computationally intensive to fit to multiple data sets (e.g. the jackknife samples) and lead to convergence issues with complex MMRM models with many parameters. Therefore, a step-wise approach based on sequential linear regression (SLR) of the outcomes at each visit was developed for the imputation model in the multiple imputation framework, but similar developments in the CMI framework are lacking. In this article, we fill this gap in the literature by proposing a SLR approach to implement RBI in the CMI framework, and justify its validity using theoretical results and simulations. We also illustrate our proposal on a real data application. [ABSTRACT FROM AUTHOR]

A controller is proposed to guide a multi-articulated robot vehicle (MARV) moving backwards, following a certain path. The ability to avoid fixed and moving obstacles is included, using the null space-based control technique to manage the conflicting tasks of following a path and avoiding obstacles. Additionally, control gains are modulated, thus reducing the risk of jackknifing. These new approaches are the contributions of the article. Results of laboratory-scale experiments with a MARV pushing one and two trailers are presented and discussed, which validate the proposed controller. Simulation results are also presented considering a MARV with three trailers, showing that the proposed controller can be adopted for larger articulated chains and another experiment that shows that it is possible to avoid moving obstacles. • Control of a multi-articulated robotic vehicle to follow a path when moving backwards. • Evasive maneuvers to avoid static or dynamic obstacles in the desired path. • Dynamic compensation to reduce the position errors for the rear of the last trailer. • Null space-based control approach hierarchic execution of complimentary subtasks. • Controller gain modulation as a tool to reduce the possibility of jackknife. [ABSTRACT FROM AUTHOR]

Summary We propose a novel empirical likelihood (EL) approach for ranked set sampling (RSS) that leverages the ranking structure and information of the RSS. Our new proposal suggests constraining the sum of the within‐stratum probabilities of each rank stratum to 1/H$$ 1/H $$, where H$$ H $$ is the number of rank strata. The use of the additional constraints eliminates the need of subjective weight selection in unbalanced RSS and facilitates a seamless extension of the method for balanced RSS to unbalanced RSS. We apply our new proposal to testing one sample population mean and evaluate its performance through a numerical study and two real‐world data sets, examining obesity from body fat data and symmetry of dental size from human tooth size data. We further consider the extension of the proposed EL method to jackknife EL. [ABSTRACT FROM AUTHOR]

The effect of the hydraulic anti-kink system on the longitudinal-yaw stability and small radius curve passing safety of the four-module single-type tram is studied. Firstly, the dynamics model of the anti-kink system is established based on the working principle of the anti-kink system, and the dynamic response of the system is analysed. Secondly, the influence of the anti-kink system on the longitudinal-yaw stability is analysed based on the longitudinal-yaw dynamics model of the four-module single-type tram. Finally, a virtual prototype of the anti-kink system and the four-module single-type low-floor tram with independent rotating wheels is established to test the longitudinal-yaw stability of the vehicle, and the curve passing safety. The results show that: the double-hinged device increases the longitudinal-yaw instability of the vehicle and is more likely to produce jackknifing phenomenon, so the stiffness of the anti-kink system should be set as much as possible to prevent the jackknifing phenomenon and ensure the safe operation of the train. By reducing the stiffness of the anti-kink system properly, the wheel-rail force during curve passing can be reduced, and thus improving vehicle safety. [ABSTRACT FROM AUTHOR]

The electrification of commercial vehicles has led to new wheel torque allocation options for propulsion and braking of articulated heavy vehicles. Each unit or axle can be individually braked or propelled whilst the other units or axles are excluded from such action. This may achieve the best energy efficiency. However, this can also lead to potential yaw stability problems such as jackknifing and trailer swing, especially under bad loading and weather conditions. This paper describes the above instabilities and introduces a nonlinear single-track model to study the vehicle dynamics of the tractor-semitrailer combination. The effects of different vehicle and environment parameters are analysed with this vehicle model. A safe operating envelope for limiting the wheel forces is obtained using this vehicle model. Since the vehicle model introduced in this paper is computationally effective, it can be run online in real vehicles, with an instantaneous safe operating envelope obtained for the momentary conditions. Thus, yaw instabilities such as jackknifing and trailer swing may be avoided. [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]

Factors associated with the habitat suitability of northern red muntjac (Muntiacus vaginalis) especially outside protected areas in the human-dominated landscape are still lacking. Fine-scale environmental variables can influence the habitat suitability of the animals. This study aimed to explore the different eco-geographic fine-scale variables for the distribution of the northern red muntjac; and predict suitable habitats using the maximum entropy (Maxent) model in the Chitwan Annapurna landscape (CHAL). The presence points of the northern red muntjac (n = 265) were collected between 2018 to 2021 using 150 transects of various lengths in four blocks. Density-based occurrence points rarify and performance-based variable selection were applied to improve the output of the model. The model was evaluated based on the area under the curve (AUC) value of operator characteristic (ROC) and analyzed on the basis of the response curve, the relative importance of variables, Jackknife test and suitability map. Results indicated the model was statistically satisfactory (mean AUC > 0.75). The distance to the nearest cropland was the most contributed variable followed by Normalized Difference Built-up Index (NDBI), distance to developed/settlement area and distance to grassland that explained suitability of Northern red muntjac. The species distribution model predicted 6.52% highly suitable and 23.77% suitable area for northern red muntjac. Therefore, this area is important for the muntjac and provides a possible alternative habitat for other wild animals outside the protected areas. Our research suggests that human dominated landscape should be prioritized in management plans for the conservation of muntjac. [ABSTRACT FROM AUTHOR]

We consider hypothesis testing in instrumental variable regression models with few included exogenous covariates but many instruments—possibly more than the number of observations. We show that a ridge-regularized version of the jackknifed Anderson and Rubin (henceforth AR) test controls asymptotic size in the presence of heteroscedasticity, and when the instruments may be arbitrarily weak. Asymptotic size control is established under weaker assumptions than those imposed for recently proposed jackknifed AR tests in the literature. Furthermore, ridge-regularization extends the scope of jackknifed AR tests to situations in which there are more instruments than observations. Monte Carlo simulations indicate that our method has favorable finite-sample size and power properties compared to recently proposed alternative approaches in the literature. An empirical application on the elasticity of substitution between immigrants and natives in the United States illustrates the usefulness of the proposed method for practitioners. [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]

Variance estimation is an important aspect in statistical inference, especially in the dependent data situations. Resampling methods are ideal for solving this problem since these do not require restrictive distributional assumptions. In this paper, we develop a novel resampling method in the Jackknife family called the stationary jackknife. It can be used to estimate the variance of a statistic in the cases where observations are from a general stationary sequence. Unlike the moving block jackknife, the stationary jackknife computes the jackknife replication by deleting a variable length block and the length has a truncated geometric distribution. Under appropriate assumptions, we can show the stationary jackknife variance estimator is a consistent estimator for the case of the sample mean and, more generally, for a class of nonlinear statistics. Further, the stationary jackknife is shown to provide reasonable variance estimation for a wider range of expected block lengths when compared with the moving block jackknife by simulation. [ABSTRACT FROM AUTHOR]

This study examines interpoint distance-based tests for random elements from probability distributions in infinite-dimensional space. Some asymptotic properties such as the limiting distributions and the asymptotic power of the Biswas–Ghosh type test (Biswas and Ghosh in J Multivar Anal 123: 160–171, 2014) are presented using the theory of U-statistic. In addition, the p-value approximation based on the jackknife variance estimators and the Welch–Satterthwaite equation is proposed. Simulation studies are conducted to evaluate the performance of the proposed test statistics in functional data analysis. The proposed tests are shown to have better power than the existing method for functional data in some situations. [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]

This paper proposes a jackknife Lagrange multiplier (JLM) test for instrumental variable regression models, which is robust to (i) many instruments, where the number of instruments may increase proportionally with the sample size, (ii) arbitrarily weak instruments, and (iii) heteroskedastic errors. In contrast to Crudu, Mellace, and Sándor (2021, Econometric Theory 37, 281–310) and Mikusheva and Sun (2021, Review of Economic Studies 89, 2663–2686), who proposed jackknife Anderson–Rubin tests that are also robust to (i)–(iii), we modify a score statistic by jackknifing and construct its heteroskedasticity robust variance estimator. Compared to the Lagrange multiplier tests by Kleibergen (2002, Econometrica 70, 1781–1803) and Moreira (2001, Tests with Correct Size when Instruments Can Be Arbitrarily Weak , Working paper) and their modification for many instruments by Hansen, Hausman, and Newey (2008, Journal of Business & Economic Statistics 26, 398–422), our JLM test is robust to heteroskedastic errors and may circumvent a possible decrease in the power function. Simulation results illustrate the desirable size and power properties of the proposed method. [ABSTRACT FROM AUTHOR]

Background: A recent breakthrough in differential network (DN) analysis of microbiome data has been realized with the advent of next-generation sequencing technologies. The DN analysis disentangles the microbial co-abundance among taxa by comparing the network properties between two or more graphs under different biological conditions. However, the existing methods to the DN analysis for microbiome data do not adjust for other clinical differences between subjects. Results: We propose a Statistical Approach via Pseudo-value Information and Estimation for Differential Network Analysis (SOHPIE-DNA) that incorporates additional covariates such as continuous age and categorical BMI. SOHPIE-DNA is a regression technique adopting jackknife pseudo-values that can be implemented readily for the analysis. We demonstrate through simulations that SOHPIE-DNA consistently reaches higher recall and F1-score, while maintaining similar precision and accuracy to existing methods (NetCoMi and MDiNE). Lastly, we apply SOHPIE-DNA on two real datasets from the American Gut Project and the Diet Exchange Study to showcase the utility. The analysis of the Diet Exchange Study is to showcase that SOHPIE-DNA can also be used to incorporate the temporal change of connectivity of taxa with the inclusion of additional covariates. As a result, our method has found taxa that are related to the prevention of intestinal inflammation and severity of fatigue in advanced metastatic cancer patients. Conclusion: SOHPIE-DNA is the first attempt of introducing the regression framework for the DN analysis in microbiome data. This enables the prediction of characteristics of a connectivity of a network with the presence of additional covariate information in the regression. The R package with a vignette of our methodology is available through the CRAN repository (https://CRAN.R-project.org/package=SOHPIE), named SOHPIE (pronounced as Sofie). The source code and user manual can be found at https://github.com/sjahnn/SOHPIE-DNA. [ABSTRACT FROM AUTHOR]

This paper analyses a general qualitative depiction of changes in the configuration of the non-linear model of a tractor-semitrailer with excessive turnability under stationary circular motions within a broad range of control parameters, such as the longitudinal velocity of motion and angle of rotation of the wheels of the controlled unit. It allows us to foresee the jackknifing effect and to estimate the conditions necessary for safe travel. The proposed analysis combines the transparent geometric approach to analyse the configuration of a tractor-semitrailer, which was developed earlier by J.P. Pauwelussen, and the ability to investigate real bifurcations of the non-linear equation of handling and the non-linear equation of folding angle tractor-semitrailer analytically. Based on this approach, we obtain new analytical dependencies that determine the boundaries of divergent loss of stability of the entire manifold of stationary states of a tractor-semitrailer model and estimates of the maximum values of the angle of folding under different values of the vehicle's longitudinal velocity. This is achieved without the prior determination of the manifold of stationary states itself. [ABSTRACT FROM AUTHOR]

Owing to the lack of prior knowledge, the accurate reconstruction of surfaces with high uncertainty is dependent on the reasonable real-time selection of the next best point (NBP) during the sampling process. In this study, a new informative criterion called the MaxCWVar weighting shape effect is proposed for NBP selection. The responses to the geometric features of the candidate locations are predicted by a back propagation neural network (BPNN), which is then used in combination with the jackknife method to estimate the candidate uncertainty. The blade cross-section sampling case is considered to validate the flexibility and effectiveness of the proposed method. A comparison with other adaptive sampling strategies shows that BPNN-based response prediction is well-suited for allocating sample points. In contrast to other NBP selection criteria, the sample point distribution recommended by the MaxCWVar criterion is preferable as it improves the reconstruction accuracy and modeling efficiency. This study promotes the exploration of metrological methods for the fast and intelligent reconstruction of complex surfaces with high uncertainty. [ABSTRACT FROM AUTHOR]

The weighted nearest neighbors (WNN) estimator has been popularly used as a flexible and easy-to-implement nonparametric tool for mean regression estimation. The bagging technique is an elegant way to form WNN estimators with weights automatically generated to the nearest neighbors (Steele 2009; Biau, Cérou, and Guyader 2010); we name the resulting estimator as the distributional nearest neighbors (DNN) for easy reference. Yet, there is a lack of distributional results for such estimator, limiting its application to statistical inference. Moreover, when the mean regression function has higher-order smoothness, DNN does not achieve the optimal nonparametric convergence rate, mainly because of the bias issue. In this work, we provide an in-depth technical analysis of the DNN, based on which we suggest a bias reduction approach for the DNN estimator by linearly combining two DNN estimators with different subsampling scales, resulting in the novel two-scale DNN (TDNN) estimator. The two-scale DNN estimator has an equivalent representation of WNN with weights admitting explicit forms and some being negative. We prove that, thanks to the use of negative weights, the two-scale DNN estimator enjoys the optimal nonparametric rate of convergence in estimating the regression function under the fourth-order smoothness condition. We further go beyond estimation and establish that the DNN and two-scale DNN are both asymptotically normal as the subsampling scales and sample size diverge to infinity. For the practical implementation, we also provide variance estimators and a distribution estimator using the jackknife and bootstrap techniques for the two-scale DNN. These estimators can be exploited for constructing valid confidence intervals for nonparametric inference of the regression function. The theoretical results and appealing finite-sample performance of the suggested two-scale DNN method are illustrated with several simulation examples and a real data application. [ABSTRACT FROM AUTHOR]

Small number of clusters combined with cluster level heterogeneity poses a great challenge for the data analysis. We have published a weighted Jackknife approach to address this issue applying weighted cluster means as the basic estimators. The current study proposes a new version of the weighted delete-one-cluster Jackknife analytic framework, which employs Ordinary Least Squares or Generalized Least Squares estimators as the fundamentals. Algorithms for computing estimated variances of the study estimators have also been derived. Wald test statistics can be further obtained, and the statistical comparison in the outcome means of two conditions is determined using the cluster permutation procedure. The simulation studies show that the proposed framework produces estimates with higher precision and improved power for statistical hypothesis testing compared to other methods. [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]

It is well established that P3 latencies increase with age. Investigating these age‐related differences requires numerous methodological decisions, resulting in pipelines of great variation. The aim of the present work was to investigate the effects of different analytical pipelines on the age‐related differences in P3 latencies in real data. Therefore, we conducted an explorative multiverse study and varied the low‐pass filter (4 Hz, 8 Hz, 16 Hz, 32 Hz, and no filter), the latency type (area vs. peak), the level of event‐related potential analysis (single participant vs. jackknifing), and the extraction method (manual vs. automated). Thirty young (18–21 years) and 30 old (50–60 years) participants completed three tasks (Nback task, Switching task, Flanker task), while an EEG was recorded. The results show that different analysis strategies can have a tremendous impact on the detection and magnitude of the age effect, with effect sizes ranging from 0% to 88% explained variance. Likewise, regarding the psychometric properties of P3 latencies, we found that the reliabilities fluctuated between rtt =.20 and 1.00, while the homogeneities ranged from rh = −.12 to.90. Based on predefined criteria, we found that the most effective pipelines relied on a manual extraction based on a single participant's data. For peak latencies, manual extraction performed well for all filters except for 4 Hz, while for area latencies, filters above 8 Hz produced desirable results. Furthermore, our findings add to the evidence that jackknifing combined with peak latencies can lead to inconclusive results. The results of our multiverse study show that different analysis strategies can have a tremendous impact on the detection and the magnitude of age‐related differences in P3 latency in cognitive tasks as well as on the psychometric properties of the data. Practical recommendations are derived from the findings. [ABSTRACT FROM AUTHOR]

We present fitcov an approach for accurate estimation of the covariance of two-point correlation functions that requires fewer mocks than the standard mock-based covariance. This can be achieved by dividing a set of mocks into jackknife regions and fitting the correction term first introduced in Mohammad & Percival (2022), such that the mean of the jackknife covariances corresponds to the one from the mocks. This extends the model beyond the shot-noise limited regime, allowing it to be used for denser samples of galaxies. We test the performance of our fitted jackknife approach, both in terms of accuracy and precision, using lognormal mocks with varying densities and approximate EZmocks mimicking the Dark Energy Spectroscopic Instrument LRG and ELG samples in the redshift range of z  = [0.8, 1.1]. We find that the Mohammad–Percival correction produces a bias in the two-point correlation function covariance matrix that grows with number density and that our fitted jackknife approach does not. We also study the effect of the covariance on the uncertainty of cosmological parameters by performing a full-shape analysis. We demonstrate that our fitted jackknife approach based on 25 mocks can recover unbiased and as precise cosmological parameters as the ones obtained from a covariance matrix based on 1000 or 1500 mocks, while the Mohammad–Percival correction produces uncertainties that are twice as large. The number of mocks required to obtain an accurate estimation of the covariance for the two-point correlation function is therefore reduced by a factor of 40–60. The fitcov code that accompanies this paper is available at this GitHub repository. [ABSTRACT FROM AUTHOR]

Randomized matrix algorithms have become workhorse tools in scientific computing and machine learning. To use these algorithms safely in applications, they should be coupled with posterior error estimates to assess the quality of the output. To meet this need, this paper proposes two diagnostics: a leave-one-out error estimator for randomized low-rank approximations and a jackknife resampling method to estimate the variance of the output of a randomized matrix computation. Both of these diagnostics are rapid to compute for randomized low-rank approximation algorithms such as the randomized SVD and randomized Nystr\"om approximation, and they provide useful information that can be used to assess the quality of the computed output and guide algorithmic parameter choices. [ABSTRACT FROM AUTHOR]

This study aims to estimate climatological cloudburst frequencies from daily precipitation sums for a dense network of 161 historical Danish stations covering the period 1914–2010, in order to reveal any systematic regional differences. We define a cloudburst day for a given station as a day when the maximum 1‐h precipitation sum exceeds a predefined threshold; we use the thresholds 15, 20 and 25 mm, corresponding to a cloudburst frequency around 0.42, 0.16 and 0.06 year−1, respectively. Supplementing the historical data, we use hourly data from a modern network and relate the daily probability of cloudburst occurrence to the corresponding daily precipitation using binary regression. This allows an estimation of the cloudburst frequency from a series of daily sums. To validate the methods, we use 33 stations that have been operating for 30 years or longer. For these stations, we demonstrate significant skill by comparing observed and estimated cloudburst frequencies with a jackknife procedure. By applying the model to the 161 historical series, we estimate climatological cloudburst frequencies throughout Denmark. We find large systematic regional variations across Denmark and these variations are much larger, but with a similar regional pattern, than obtained by previous work. We suggest applying the approach to the historical daily precipitation series that exist across the world. [ABSTRACT FROM AUTHOR]

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]

The linear regression model explores the relationship between the dependent variable and the independent variables. The ordinary least squared estimator (OLSE) is widely applicable to estimate the parameters of the model. However, OLSE suffered a breakdown when the independent variables are linearly dependent- a condition called multicollinearity. The KibriaLukman estimator (KLE) was suggested as an alternative to the OLSE and some other estimators (ridge and Liu estimators). In this paper, we developed a Jackknifed version of the Kibria-Lukman estimator- the estimator is named the Jackknifed KL estimator (JKLE). We derived the statistical properties of the new estimator and compared it theoretically with the KLE and some other existing estimators. Theoretically, the result revealed that JKLE possesses the lowest MSE when compared with the KLE and some other existing estimators. Finally, JKLE reduced the bias and the mean squared error (MSE) of KLE in both simulation and real-life analysis. JKLE dominates other methods considered in this study. [ABSTRACT FROM AUTHOR]

The negative binomial regression model is a widely adopted approach when dealing with dependent variables that consist of non-negative integers or counts. This model serves as an alternative regression technique for addressing issues related to overdispersion in count data. Typically, the maximum likelihood estimator is employed to estimate the parameters of the negative binomial regression model. However, the maximum likelihood estimator can be highly sensitive to multicollinearity, leading to unreliable results. To eliminate the adverse effects of multicollinearity in the negative binomial regression model, we propose the use of a jackknife version of the Kibria–Lukman estimator. In this study, we conducted a theoretical comparison between the proposed jackknife Kibria–Lukman negative binomial regression estimator and several existing estimators documented in the literature. To assess the performance of the proposed estimator, we conducted two simulation studies and performed a real data application. The results from both the simulation studies and the real data application consistently demonstrated that the proposed jackknife Kibria–Lukman negative binomial regression estimator outperforms other estimators. [ABSTRACT FROM AUTHOR]