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In this paper, the Bayesian and Bayesian shrinkage estimators of the scale parameter of two-parameter exponential distribution are provided based on the square error and Al-Bayyati loss functions and right censoring. Both informative (inverse-Gamma) and non-informative (quasi-density) priors are considered for the scale parameter of two-parameter exponential distribution. The estimators from different loss functions are evaluated against each other via the risk and risk efficiency measures. Based on the simulation scheme and real data set, we compare the proposed estimators under both loss functions with risk and risk efficiency measures, which lead to efficiency of the Bayesian shrinkage estimates under informative prior. In real data analysis, Bayesian and Bayesian shrinkage estimation of the scale parameter for the flood stages data set is considered with both square error and Al-Bayyati loss functions under the right censoring scheme. [ABSTRACT FROM AUTHOR]

This paper provides a new perspective for robust estimation and inference methods based on Huber regression. An efficient distributed learning with sparsity is proposed, in which the observations are randomly divided among different machines. We modify the proximal alternating direction method of multiplies (ADMM) algorithm to calculate the sparse penalized Huber regression. The convergence property of the algorithm is established. Computationally, our proposed approach requires only a central machine to solve a SCAD or adaptive lasso penalized M-estimation problem, and other node machines to calculate gradients based on local datasets. In terms of communication, the estimation error of our method decreases to that of the centralized method in several rounds of communication. Simulation studies are conducted to evaluate the finite-sample performance of our proposed method. The empirical study shows that our method has good practicability in the practice of a Communities and Crime analysis. [ABSTRACT FROM AUTHOR]

Machine learning methods have been extensively used in survival analysis. SurvivalBoost - a machine-learning-based survival regression algorithm, focused on Elastic-net-Type penalized semiparametric Cox regression model on XGBoost and random survival forests, has been verified its superior prediction performance on real and simulated datasets. Whereas the interpretability is remain undiscovered. This paper discusses the interpretability of this algorithm upon using the Shapley Additive Explanation (SHAP) value. It is illustrated that the algorithm can be more effective to guide the diagnosis and practice of survival analysis. [ABSTRACT FROM AUTHOR]

The portfolio optimization problem can be reformulated by a regression model. Mean-variance portfolios, which are constructed using the sample mean and covariance matrix of asset returns can be considered as a function of the ordinary least squares estimator of the linear regression coefficients. It is well known that this estimator has several drawbacks. In particular many researchers have pointed out its high sensitivity in the presence of outliers and its loss of efficiency in the presence of small deviations from the normality assumption. In this paper we propose a novel regression approach for optimizing portfolios by means of quantile regression models. The proposed portfolios are constructed using certain robust and distribution-free estimators and can be obtained by solving a single linear program, where estimation and portfolio optimization are performed in a single step. Our numerical results on simulated and empirical data confirm that the proposed portfolios behave much better than the traditional mean-variance portfolio, in terms of the Sharpe ratio and expected loss in utility. [ABSTRACT FROM AUTHOR]

AbstractSemiparametric models (SM) are an important tool in modeling environmental data where generally a covariate presents an unknown nonlinear behavior. Usually, the error component is assumed to follow a normal distribution. However, in some situations, the response variable is skewed and heavy-tailed. This paper aims to extend the SMs allowing the errors to follow a skew scale mixture of normal distributions, increasing the model’s flexibility. In particular, we develop the EM algorithm for the proposed model, diagnostic analysis via global, local influence, and generalized leverage. A simulation study is also conducted to evaluate the efficiency of the EM algorithm. Finally, a suitable transformation is applied in a data set on ragweed pollen concentration to illustrate the utility of the proposed model. [ABSTRACT FROM AUTHOR]

AbstractIn epidemiological cohort studies, the relative risk is a key measure to gauge the connection between two treatments or exposures. It quantifies the proportional change in the risk of disease due to the application of a specific treatment. However, the conventional methods for calculating relative risk, available in widely-used software, might yield inaccurate results when applied to correlated binary data from studies conducted over time or in clusters. Recently, various techniques have been proposed to estimate the risk ratio for correlated binary data. However, some methods exhibit a tradeoff between maintaining accurate coverage probability (CP) and ensuring an appropriate interval width or location. This paper introduces a new approach to confidently estimating the risk ratio using a hybrid method. This hybrid method combines two distinct confidence intervals (CIs) derived from single risk rates to establish a unified confidence interval for their ratio. Furthermore, we present a methodology to construct a confidence interval for the risk ratio, which builds upon established methods for correlated binary data. This extension incorporates principles such as the design effect and adequate sample sizes commonly used in representative sample surveys. An extensive simulation study is conducted to evaluate the effectiveness of these proposed methods. The performance of the methods is thoroughly examined in various scenarios. Additionally, the practicality of the proposed methods is showcased through three real-life examples. These examples involve comparing the side effects of low-dose tricyclic antidepressants with a placebo, assessing the efficacy of a treatment group in a teratological experiment, and evaluating the efficiency of active drugs in curing infections during clinical trials. [ABSTRACT FROM AUTHOR]

AbstractIn this paper, we propose a flexible cure rate survival model by assuming the number of competing causes, related to the event of interest, to follow generalized Poisson distribution. The generalized Poisson distribution has several important properties, e.g. it can effectively model both underdispersed (mean > variance) and overdispersed (mean < variance) mechanisms present in the data. Further, it includes the promotion time cure model as a special case. In this work, for a non-cure subject, we model the time to event of interest with the piecewise exponential distribution. We emphasize that the piecewise exponential distribution has a greater flexibility to model failure times, and can be considered as a distribution-free alternative to the parametric distributions based assumptions. Inferences for the model parameters are considered via full Bayesian analysis. Further, a detailed simulation study is performed with different parameter settings, sample sizes and censoring percentages to study the behavior of the estimators. Finally, a data set from the medical area is analyzed for further illustration. [ABSTRACT FROM AUTHOR]

AbstractInspection of raw materials, semi-finished products or final products is an important part of a quality assurance system. Acceptance sampling is a procedure used to decide either to accept or reject suppliers’ submitted lots in accordance with a specific standard. In this manuscript, designing acceptance sampling plans for lots with polynomial profile as quality characteristic is considered. To use previous lot information on deciding for accept or reject the available lot, exponentially weighted moving average (EWMA) statistic based on process yield index (Spk) of polynomial profiles with two-sided specification limits is applied. For this purpose, three acceptance sampling plans of repetitive group sampling (RGS), resubmitted and also combined RGS-resubmitted plans are developed in this paper. The Parameters of the proposed plans are determined using non-linear optimization model. Performance of the proposed acceptance sampling plans are compared using numerical methods and Monte-Carlo simulations. Simulation results emphasize that the proposed combined sampling plan mostly requires less average sampling number (ASN) and consequently leads to decreasing inspection time and costs. The application of the proposed combined plan is also demonstrated using a real case. [ABSTRACT FROM AUTHOR]

AbstractDiscrete approximations of continuous random variables play a crucial role in various areas of research and application, offering advantages in computational efficiency, interpretability, and modeling flexibility. This paper investigates discrete representations of continuous random variables using the mean-squared error criterion (MSE-RPs) and the inverse transformation method. We introduce a novel discrete approximation to the normal distribution that surpasses conventional MSE-RPs obtained from the normal density, particularly in matching lower-order moments. Furthermore, we propose a two-step generalized inverse transformation method to generate approximate MSE-RPs of random variables, inspired by the remarkable performance of the inverse transformation method in statistical simulation. Overall, the generalized inverse transformation method offers a more efficient and reliable alternative for obtaining discrete approximations to target continuous distributions, especially in scenarios where explicit computation and derivation of density functions are challenging or computationally expensive. Moreover, we extend our investigation to the case where the target distribution is a convolution of two random variables, thereby expanding the applicability of our proposed method. Furthermore, our findings hold potential applications in Monte Carlo simulation and resampling techniques. [ABSTRACT FROM AUTHOR]

AbstractToday, manufacturers face two challenges: the financial limitation of sampling and the large number of study quality characteristics. In such situations, the problem dimension is usually larger than the sample size, which is known in the literature of statistical quality control as a high dimensional process. The use of conventional multivariate charts to monitor the covariance matrix of such processes is not possible for two reasons: (1) the non-reversibility of the sample covariance matrix, (2) the possibility of the occurrence of sparse shifts in which only a few elements of the covariance matrix are affected. This paper focuses on Phase II monitoring of the covariance matrix of high-dimensional processes based on integrating the ridge penalized likelihood ratio (RPLR) statistic and the combined DS-VSS sampling method, in which DS and VSS features are used concurrently. The performance of the proposed DS-VSS RPLR control chart is compared with the RPLR one in terms of three metrics of the average run length, standard deviation of the run length, and expected value of sample size under three types of joint diagonal/off-diagonal, diagonal and off-diagonal shift patterns. The results show that the DS-VSS scheme is more sensitive than the RPLR in detecting both sparse and non- sparse changes. [ABSTRACT FROM AUTHOR]

AbstractThis paper proposes two new estimation methods to fit a multiple structural measurement error model when all variables are subject to errors. The new estimation methods were extensions of the Wald estimation method, one is the weighted grouping method, and the other is the iterative method. A Monte Carlo experiment is performed to investigate the performance of the new estimators compared with the classical estimation methods; the Maximum Likelihood Estimator and Method of Moment, in terms of root mean square error and its bias. The simulation outcomes demonstrated that the suggested estimators are more effective than conventional estimators. In addition, real data analysis is discussed to examine the relationship between the national gross domestic product, unemployment rate, and human development index after applying the two proposed estimation methods. [ABSTRACT FROM AUTHOR]

AbstractInformative dropout occurs when the subject’s follow-up time depends on the response process, even conditional on the covariates process. Most existing works for the regression analysis of asynchronous longitudinal data presume that dropouts are virtually non-informative. In this paper, we propose kernel-weighted estimating equations to accommodate asynchronous measurement and informative dropout simultaneously. We specify a semiparametric linear regression model for the response process and an accelerated failure time model for the dropout process. Unlike the fully specified parametric or nonparametric model in most existing literature, the proposed method does not require model specification for the joint distribution. To deal with the informative dropout, an artificial censoring device is employed. Besides, the observation process is allowed to depend on the covariate process. The proposed estimators are shown to be consistent and asymptotically normally distributed. We conduct a series of simulation studies to assess the finite sample performance of the proposed estimators. Applying the suggested approaches to the Study of Women’s Health Across the Nation indicates a significant negative association between follicle-stimulating hormones and triglycerides. [ABSTRACT FROM AUTHOR]

AbstractIn this paper, a new bivariate random coefficient integer-valued autoregressive process based on modified negative binomial operator with dependent innovations is proposed. Basic probabilistic and statistical properties of this model are derived. To estimate unknown parameters, Yule-Walker, conditional least squares and conditional maximum likelihood methods are considered and evaluated by Monte Carlo simulations. Asymptotic properties of the estimators are derived. Moreover, coherent forecasting and possible extension of the proposed model is provided. Finally, the proposed model is applied to the monthly crime datasets and compared with other models. [ABSTRACT FROM AUTHOR]

Percentile modification concerns with using only fraction of the sample observations in computation of the test statistic. The modification improves power of rank based tests given appropriate amount of percentile modification is performed. This paper addresses the problem of deciding amount of percentile modification in context of two sample, multivariate scale problem using data depth. We propose an adaptive test which decides amount of modification based on tail heaviness of the data. As a second approach, we define three test statistics on a group of percentile modified statistics using different combining functions, viz. a quadratic form, a maximum-type and a sum-type. With this strategy, the task of choosing a single optimum value as an amount of percentile modification becomes irrelevant. Monte-Carlo simulation is used to perform comparative power study. Adaptive test as well as sum-type and maximum-type statistics based on a group of percentile modified statistics yield attractive powers whereas quadratic form statistics do not show promising results. [ABSTRACT FROM AUTHOR]

Principal curves are natural generalizations of principal lines arising as first principal components in the Principal Component Analysis. They can be characterized—from a stochastic point of view—as so-called self-consistent curves based on the conditional expectation and—from the variational-calculus point of view—as saddle points of the expected difference of a random variable and its projection onto some curve, where the current curve acts as argument of the energy functional. Beyond that, Duchamp and Stützle (1993, 1996) showed that planar curves can be computed as solutions of a system of ordinary differential equations. The aim of this paper is to generalize this characterization of principal curves to R d with d ≥ 3. Having derived such a dynamical system, we provide several examples for principal curves related to uniform distribution on certain domains in R 3. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new class of heterogeneous spatial autoregressive models (heterogeneous SAR models) where the variance parameters are modeled in terms of covariates. In order to estimate the model parameters, as well as their corresponding standard error estimates, we proposed a computational efficient MCMC method which combines the Gibbs sampler with Metropolis-Hastings algorithm. The proposed estimate method is illustrated through numerous simulations and is applied to the Boston housing data. [ABSTRACT FROM AUTHOR]

Numerous variable selection techniques have been developed for complete high-dimensional data but very few of them for censored data. The techniques for complete data must be modified if censoring is present. In this paper, we consider the variable selection technique for accelerated failure time (AFT) models by extending the ranking-based variable selection (RBVS) algorithm and its iterative procedure as proposed in the work of Baranowski et al. through the Stute's weighted least square technique. Simulation studies are conducted to demonstrate the performance of the proposed methods. We further illustrate the performance of this method with a mantle cell lymphoma microarray example. When there is no correlation among the covariates, the proposed method outperforms the iterative sure independence screening and stability selection methods in terms of overall performance for high-dimensional data. Real data analysis also suggests that the proposed method can be chosen for high-dimensional censored data analysis in parallel to other methods in the literature. [ABSTRACT FROM AUTHOR]

Sum scores from questionnaire data are frequently analyzed under the normality assumption which is not always tenable due to for instance the skewness of the distribution, or the discreteness of the sum scores for small number of items. Alternatively, an ordinal regression analysis can be applied, but this approach seems appropriate only for very small number of items. The current state-of-the-art approach is to apply a beta-binomial model, though the beta-binomial model does not simply connect to item-response theory models that may describe the underlying items of the questionnaire, and it is more cumbersome to fit to multi domain sum scores or repeated longitudinal single sum scores. This paper proposes a normal-probit-binomial model for repeated sum scores that has an item level interpretation under certain assumptions without having to analyze the individual items. All parameters, the temporal correlation coefficients, and the mean difficulty parameter were almost unbiasedly estimated, irrespective of the set of item difficulty parameters. The coverage probability of the 95% confidence intervals were close to the nominal level, except for the correlation coefficients that were slightly liberal. Our model performed slightly better than the beta-binomial model on cross-sectional data and it handles missing items easily. [ABSTRACT FROM AUTHOR]

This paper proposes two integer linear programming formulations to solve the optimal stratification problem (OSP). In this problem, once given the number of strata and the total sample size, the cutoff points and sample allocation should be determined jointly to minimize an expression of variance and to solve the OSP corresponding to an integer nonlinear optimization problem. One proposed formulation determines the optimal cutoff points considering classical allocation methods from the literature, and a second formulation produces the global optimum regarding the determination of the cutoff points and the sample allocation to the strata. Both formulations were implemented using Gurobi solver and applied to a set of 20 datasets from the literature, with population sizes ranging from 91 to 16,057, considering six different scenarios concerning the number of strata and sample sizes. The results obtained indicate that the formulations are a good alternative for the resolution of the OSP. [ABSTRACT FROM AUTHOR]

In this paper, we establish the complete moment convergence for a field of martingale difference random variables, weakly upper bounded by a random variable. The results generalize and extend the complete convergences for non-identically distributed martingale-difference random fields to the case of complete moment convergences. [ABSTRACT FROM AUTHOR]

In this paper we introduce first-order spatial random coefficient non-negative integer-valued autoregressive (SRCINAR(1,1)) model to fit the spatial count data on a two-dimensional regular lattice. We use a thinning operator in order to define the processes. The mean, variance and autocorrelation function of the model are derived. Three methods (Yule-Walker, Conditional least squares and Conditional maximum likelihood) for the estimation of the parameters of the model are discussed and are compared with respect to the root mean squared error (RMSE), in a simulation study. Finally, SRCINAR(1,1) model is applied to a real data set of striga counts at the ICRISAT Sahelian Center near Niamey (Niger). [ABSTRACT FROM AUTHOR]

This paper is concerned with investigating the adequacy of using the p-value as an estimator for the set specified by the null hypothesis in the Exponential distribution. It is shown that the p-value is an admissible estimator in the one-sided test of the location parameter. When the one-sided test of the scale parameter is considered, the p-value is found to be a generalized Bayes estimator with infinite Bayes risk. However, it is very difficult to find an estimator that dominates it. When the parameter space is restricted, the modified p-value is an admissible estimator in the one-sided test of the scale parameter and performs better than the usual p-value. Although the usual p-value is generally inadmissible in the two-sided test, it can be useful as an estimator in this type of test for the scale parameter. [ABSTRACT FROM AUTHOR]

In multiple Regression Model the absence of multicollinearity is essential. The presence of multicollinearity is often caused by including too many (highly correlated) regressors and in this case, the estimates tend to be less precise. For this reason, varies methods have been introduced to solve these problems caused by the existence of multicollinearity. In this paper, a new method to estimate the ridge parameter, based on the ridge trace and an analytical method borrowed from Generalized Maximum Tsallis Entropy, is presented and we call that the Ridge GMET2 estimator. The performance of the new estimator is illustrated through a Monte Carlo simulation study. We compared the Ridge GMET2, Ridge GME and OLS estimators. Mean square error of Ridge GMET2 estimates, is less than corresponding for Ridge-GME and OLS estimates. In some case also, the value of the Ridge-GME and Ridge-GMET2 estimators are nearer, since Tsallis entropy does not depend on the logarithm unlike, the Shannon entropy, so that it is a substantial point that we prefer the Ridge-GMET2 estimator. [ABSTRACT FROM AUTHOR]

Multiple hypotheses testing has been widely studied in the literature due to its broad applicability, particularly in the fields of biogenetics and astrogeology. The false discovery rate (FDR) is a useful error control criterion for large-scale multiple hypotheses, which is loosely defined as the expected proportion of false positives among all rejected hypotheses. In this paper, we propose a Gaussian mixture model (GMM) to fit the distribution of the Z-value statistics, including the nulls distribution as a fixed component. The nulls proportion and the real nulls distribution are estimated by the fitted GMM simultaneously. A GMM-based procedure is then proposed to minimize the false nondiscovery rate (FNR) subject to a constraint on the FDR. Both simulations and real data analysis show that the GMM-based procedure performs considerably well comparing to some competitors. [ABSTRACT FROM AUTHOR]

AbstractThe two-parameter Birnbaum-Saunders distribution is widely used in reliability analysis. In this paper, several Birnbaum-Saunders parameters estimation using simple random sampling (SRS), ranked set sampling (RSS) and a RSS version based on the order statistic that maximizes the Fisher information for a fixed set size (RSSF) are respectively considered. Theoretical properties of the suggested estimators are compared with its counterpart estimators using SRS by numerical simulation and a real data application. The numerical results and real data application show that the suggested estimators using RSS and RSSF can be real competitors for those using SRS. [ABSTRACT FROM AUTHOR]

AbstractThis paper presents a Bayesian nonparametric model for clustering datasets with continuous, ordinal, and nominal variables. The ordinal and nominal variables are treated using the latent variables framework based on the multivariate probit and the multinomial probit models. Combining the continuous variables with the latent continuous variables allows us to jointly model a set of mixed-type variables via the Dirichlet process Gaussian mixture model. The use of hierarchical shrinkage prior on the component means leads to improved clustering performances and provides an intuitive way to identify relevant clustering variables. The numerical results on simulated and real data illustrate the applicability of the proposed model. [ABSTRACT FROM AUTHOR]

AbstractThe exponentially weighted moving average (EWMA) charts are widely used memory-type charts for monitoring small to moderate shifts in process parameters. However, the performance of the EWMA chart has been improved over time due to various modifications and enhancements. This paper proposes two modified EWMA (M‐EWMA) charts to monitor process dispersion. The upper-sided modified EWMA chart is denoted by M‐EWMAU, while a lower-sided modified EWMA chart is symbolized as the M‐EWMAL chart. Monte Carlo simulations determine the proposed schemes’ run length (RL) properties in zero- and steady-state scenarios. The proposed upper- and lower-sided M‐EWMA charts are compared to the upper- and lower-sided CH‐EWMA and SJ-EWMA charts. The comparisons reveal that the proposed M-EWMA charts have better detection ability than the upper- and lower-sided CH-EWMA, and SJ-EWMA charts, respectively. Finally, a real-life application is provided to illustrate the implementation of the upper-sided M-EWMA and CH-EWMA charts practically in both zero-state and steady-state cases. [ABSTRACT FROM AUTHOR]

In this paper, we consider a competitive risk scenario in which the initial number of competing risks, assumed to follow a shifted Poisson distribution, is subject to a destructive element. In such settings, both the number of initial risks and risks remaining active after destruction represent missing data. Assuming the population of interest to have a cure component and the form of the data as interval-censored, we extend the destructive shifted Poisson cure model with Weibull lifetimes to accommodate interval-censored data and develop an efficient expectation maximization algorithm for this model. By using the conditional distributions of the missing data, the conditional expected complete log-likelihood function is decomposed into simpler functions which are then maximized independently. An extensive simulation study is carried out to demonstrate the performance of the proposed estimation method through calculated bias, root mean square error, and coverage probability of the asymptotic confidence interval. Also considered is the efficacy of the proposed EM algorithm as compared to direct maximization of the observed log-likelihood function. Finally, data from a crime recidivism study is analyzed for illustrative purpose. [ABSTRACT FROM AUTHOR]

Smog in China has been a major issue in recent years. As the main component of smog, PM 2.5 has received a lot of attention from the public, as the pollution caused by PM 2.5 is believed to have negative impacts in many aspects. Accordingly, modeling PM 2.5 concentrations has become research of interest for the sake of future prediction and control. Based on the data collected from monitoring stations nationwide, we find that PM 2.5 concentrations show both spatial and temporal dependency. In this paper, we adopt a grouped spatial-temporal model to depict the distribution of PM 2.5 , capturing the spatial heterogeneity in the patterns of PM 2.5 concentrations. An estimation method based on the EM algorithm is used since the group label assignment is unknown, and the results are further explained. Finally, an outlier detection procedure based on the grouped spatial-temporal model is presented. [ABSTRACT FROM AUTHOR]

In this paper, we focus on Bayesian estimation of the parameters in the geometric process (GP) in which the first occurrence time of an event is assumed to have Weibull distribution. The Bayesian estimators are derived based on both symmetric (Squared Error) and asymmetric (General Entropy, LINEX) loss functions. Since the Bayesian estimators of unknown parameters cannot be obtained analytically, Lindley's approximation and the Markov Chain Monte Carlo (MCMC) methods are applied to compute the Bayesian estimates. Furthermore, by using the MCMC methods, credible intervals of the parameters are constructed. Maximum likelihood (ML) estimators are also derived for unknown parameters. The confidence intervals of the parameters are obtained based on an asymptotic distribution of ML estimators. Moreover, the performances of the proposed Bayesian estimators are compared with the corresponding ML, modified moment and modified maximum likelihood estimators through an extensive simulation study. Finally, analyses of two different real data sets are presented for illustrative purposes. [ABSTRACT FROM AUTHOR]

Finite mixture of linear regression (FMLR) models are an efficient tool to fit the unobserved heterogeneous relationships. The parameter estimation of FMLR models is usually based on the normality assumption, but it is very sensitive to outliers. Meanwhile, the traditional robust methods often need to assume a specific error distribution, and are not adaptive to dataset. In this paper, a robust estimation procedure for FMLR models is proposed by assuming that the error terms follow an asymmetric exponential power distribution, including normal distribution, skew-normal distribution, generalized error distribution, Laplace distribution, asymmetric Laplace distribution, and uniform distribution as special cases. The proposed method can select the suitable loss function from a broad class in a data driven fashion. Under some conditions, the asymptotic properties of proposed method are established. In addition, an efficient EM algorithm is introduced to implement the proposed methodology. The finite sample performance of the proposed approach is illustrated via some numerical simulations. Finally, we apply the proposed methodology to analyze a tone perception data. [ABSTRACT FROM AUTHOR]

The parameters of generalized linear models (GLMs) are usually estimated by the maximum likelihood estimator (MLE) which is known to be asymptotically efficient. But the MLE is computed using a Newton-Raphson-type algorithm which is time-consuming for a large number of variables or modalities, or a large sample size. An alternative closed-form estimator is proposed in this paper in the case of categorical explanatory variables. Asymptotic properties of the alternative estimator is studied. The performances in terms of both computation time and asymptotic variance of the proposed estimator are compared with the MLE for a Gamma distributed GLM. [ABSTRACT FROM AUTHOR]

This paper studies the hypothesis testing problem where the null hypothesis is that a time series is an unit root process and the alternative hypothesis is that there is a change point so that the time series shifts from an unit root process to a long memory process or vice verse. We propose a residual based Dickey-Fuller type ratio statistic and derive its null distribution. We also establish the limiting distribution of the test statistic under the long memory process with no change point hypothesis. In particular, a sieve bootstrap method is designed to determine the critical value of the test statistic. Simulations show that the new test can control the empirical size well, even for the heavy-tailed long memory process. Our proposed test also gives competitive empirical power compared to the well known CUSUM of squares-based test. Finally, the validity of the new test is illustrated by a set of foreign exchange rate data between RMB and U.S. dollars. [ABSTRACT FROM AUTHOR]

Interval-valued data have been widely used in both academic and industry research areas. With the development of computational statistics, the Bayesian methods are growing rapidly. Based on the existing theoretical researches, this paper tries to establish a Bayesian framework for interval-valued data, which contains the determination of Jeffreys' prior, posterior inferences, and posterior predictive checking methods. First, Jeffreys' prior for interval-valued data is proposed for the first time. Then, the posterior conditional distribution is derived, and posterior samples are obtained by using Gibbs sampling methods. Based on posterior samples, we obtain the Bayesian point and credible interval estimations for interval-valued data. Finally, we propose a posterior predictive checking method for interval-valued data based on novel test quantities. If the posterior predictive checking method shows that the data do not meet the distribution assumptions, we suggest the use of a data transformation. The effectiveness of our method is demonstrated by simulations and two cardiological data sets. [ABSTRACT FROM AUTHOR]

This paper investigates theoretical and numerical asymptotic properties of a nonparametric M-estimator's regression function when the data are left truncated and associated. Using specific tools to this weak dependence, we study the strong uniform consistency of the proposed estimator and give its rate of convergence. A large Monte Carlo simulation study is carried out to comfort the good behavior of the M-estimator for different sample sizes and different truncation rates: First we show that the proposed estimator performs better than the Nadaraya-Watson estimator by looking at their respective closeness to the true univariate and bivariate regression function. Thereafter and to highlight the robustness of our estimator, we consider a regression model with a heavy-tailed error distribution and we compare the global mean square error of the two estimators. Finally, we study the behavior of the two estimators in the presence of outliers using the influence function to show the superiority of the M-estimator. [ABSTRACT FROM AUTHOR]

In this paper we study point processes on the complex plane and illustrate their uses in several statistical areas, where the quantities of interest requiring estimation involve Fourier expansions. In particular, for any problem where we can describe a quantity in terms of its Fourier expansion, we propose modeling the coefficients of the expansion using a point process on the complex plane. We utilize the Poisson complex point process and model its intensity function using log-linear and mixture models. The proposed models are exemplified via applications to general density approximation, via modeling of the characteristic function, and time series analysis, via modeling of the spectral density. [ABSTRACT FROM AUTHOR]

In this paper, we are interested in solving backward doubly stochastic differential equations in Lp, for any p ∈ (1 , 2) , when the coefficients are continuous with stochastic linear growth. Via approximation and comparison theorem, the existence of L p − minimal and L p − maximal solutions are obtained. [ABSTRACT FROM AUTHOR]

In this paper, we consider a transformation in a random variable which follows a bimodal Birnbaum-Saunders distribution. We propose the unit-bimodal Birnbaum-Saunders (UBBS) distribution and investigate some of its important properties, like cumulative distribution function, moments, survival function and risk function. We apply the UBBS distribution to censored data inflated at zero and one. We used the maximum likelihood approach for parameter estimation and to compare the models. Given the flexibility in UBBS distribution modes, our proposal performs best in beta regression models with zero and/or one excess. [ABSTRACT FROM AUTHOR]

Redundant is used to improve the reliability of a given system and to ensure that it is available to fulfill its duty during a mission time. This paper proposes an algorithmic approach for solving RAPs when component lifetimes are either independent and heterogeneous under a general setting. Two common active and standby schemes for allocations, are considered. Moreover, a new stochastic order is proposed and applied for comparison purposes. Various illustrative examples are also analyzed. This method can be implemented for engineering system networks. [ABSTRACT FROM AUTHOR]

In multiple linear regressions, it is known that least-squares estimates of the parameters are likely to be too large in absolute value and possibly of wrong sign, if explanatory variables are correlated. To reduce the undesirable effects of collinearity, the ridge estimator has been proposed as an alternative method to the least squares estimator. The biggest debate with the ridge estimator is the selection of the regularization parameter. Several methods for the selection of the regularization parameter have been discussed. Although most of these methods are based on minimizing the mean square error of the ridge estimator, bootstrap resampling method is also proposed to provide an optimal regularization parameter which gives an estimate of mean square error of prediction. The purpose of this paper is to provide a comprehensive study of regularization parameter selection methods which consider bootstrap approach as well as estimation and prediction approaches. The paper concludes with application of these procedures to simulation studies and real data. [ABSTRACT FROM AUTHOR]

The inverse moment's research can be used in many fields such as risk evaluation and insurance mathematics. In this paper, we consider the weighted inverse moment model based on asymptotically almost negatively associated (AANA, in short) sequences. Under some weak condition, we obtain the asymptotic approximation of inverse moments and its convergence rate. As applications of inverse moments, we study the random ratio models which contain the change-point detection models, and obtain the asymptotic moment approximation of random ratio and its convergence rate. Our conditions of inverse moment and random ratio models are very weaker than the existing models. In order to test our results, we do some simulations and real data analysis in this paper. Our results improve and general the existing works. [ABSTRACT FROM AUTHOR]

Let Graph HT ht be a sample from a lognormal distribution with parameters I SB i sb i and Graph HT ht Graph HT ht Assuming that both samples are independent, Singhasomboona, Panichkitkosolkula and Volodin (2020) have addressed the problem of interval estimating the ratio of the medians of two lognormal distributions. Let Graph HT ht denote the (mean, variance) based on Graph HT ht One of the best CI for Graph HT ht is known as the Welch approximate degrees of freedom CI (Welch [2]). [Extracted from the article]

AbstractThis article studies the Bayesian estimation of the inequality-constrained regression model under a balanced loss function. The usual Bayes estimator is often involved in some complex integrals and has no explicit expression, which causes the corresponding properties be difficult to describe. Based on the idea of linear Bayes method suggested by Rao (1973), the present paper constructs a linear Bayes estimator for the regression parameters without specify their specific prior distributions. It is proved that the proposed linear Bayes estimator outperforms the corresponding least squares estimator, and numerical simulations show that when there is collinearity in design matrix, the linear Bayes estimator performs better than the usual Bayes estimator. [ABSTRACT FROM AUTHOR]

AbstractIn this paper, the marginal distribution of second-order concomitants of order statistics (SCOSs) from the Cambanis family is determined. An advantageous recurrence relation between single moments of SCOSs and concomitants of order statistics (COSs) is established based on the Cambanis family. We also use this family to derive an elegant beneficial recurrence relation between single moments of the SCOSs. Some information measures, such as Shannon differential entropy, differential extropy, and negative cumulative extropy (NCEX) of SCOSs based on this family, are investigated. Furthermore, we present some numerical examples to back up the theoretical findings. In addition, a set of bivariate data from the real world was examined. Finally, an estimate of a marginal variable’s scale parameter in the copula Cambanis family is obtained. [ABSTRACT FROM AUTHOR]

AbstractMost of existing methods for analyzing unreplicated two-level factorial designs need the assumption of effect sparsity and only perform well when the effectssparsity assumption holds. The effects-sparsity assumption is frequently true, but it is not always true. This paper proposes a new method that needs not the effects-sparsity assumption and has the potential for detecting up to m-1 active effects, in which m is the number of effects under study. The proposed method is illustrated by two unreplicated factorial designs appeared in the literature. An extensive Monte Carlo comparison study, based on 100,000 replications, is carried out to compare the proposed method with another four popular and powerful existing objective methods. The simulation study shows that the proposed method has more power than the remainder four compared methods in most of the conditions under study. [ABSTRACT FROM AUTHOR]

The coefficient of variation (CV) is one of the most important quality characteristics in industrial applications. There have been some control charts for monitoring this dimensionless and normalized characteristic. This paper presents three double exponentially weighted moving average (DEWMA) charts for monitoring the CV. Many numerical simulations are performed and the results are given in several tables to show the properties of the proposed DEWMA CV charts. Through comparisons with other existing exponentially weighted moving average (EWMA) CV charts using the average run length (ARL) metric, it is shown that the proposed DEWMA CV charts perform better than the existing EWMA CV charts for small shifts, especially when the smoothing parameter increases. In addition, a detailed comparison among the proposed three DEWMA CV charts is also presented. A real date example from industry is used to show the implementation of the proposed charts. [ABSTRACT FROM AUTHOR]

The minimum covariance determinant (MCD) estimate is an important subsample method in robust statistics. It is commonly used to estimate parameters of multivariate normal distributions when outliers exist because of its good robustness properties. However, MCD has some disadvantages including low efficiency when there is no outliers and poor performance when there are clustered outliers. This paper first introduces an adaptive subsample method, and shows that the adaptive MCD estimator can possess both full asymptotic efficiency and maximum breakdown value. We then propose a minimum distance subsample estimate to handle the situations where there are clustered outliers. Simulation results indicate that the adaptive version of the minimum distance subsample estimate has satisfactory performance for various types of outliers. [ABSTRACT FROM AUTHOR]

Linear Mixed Effects (LME) models have been widely applied in clustered data analysis in many areas including marketing research, clinical trials, and biomedical studies. Inference can be conducted using maximum likelihood approach if assuming Normal distributions on the random effects. However, in many applications of economy, business and medicine, it is often essential to impose constraints on the regression parameters after taking their real-world interpretations into account. Therefore, in this paper we extend the classical (unconstrained) LME models to allow for sign constraints on its overall coefficients. We propose to assume a symmetric doubly truncated Normal (SDTN) distribution on the random effects instead of the unconstrained Normal distribution which is often found in classical literature. With the aforementioned change, difficulty has dramatically increased as the exact distribution of the dependent variable becomes analytically intractable. We then develop likelihood-based approaches to estimate the unknown model parameters utilizing the approximation of its exact distribution. Simulation studies have shown that the proposed constrained model not only improves real-world interpretations of results, but also achieves satisfactory performance on model fits as compared to the existing model. [ABSTRACT FROM AUTHOR]

There have been some advances in multivariate control charts in recent years. This paper presents a new simultaneous scheme for monitoring both the mean and variability of a multivariate normal process in a single chart, which is developed by improving and modifying another recently proposed scheme. We not only propose a new control scheme but also make it adaptive by varying all control chart parameters. Our scheme, for the first time, considers the process variability in two forms: "covariance matrix" and "multivariate coefficient of variation (MCV)". This scheme, again for the first time, considers simultaneous monitoring of the MCV with another process parameter (in our case, the mean vector). In addition, we develop a Markov chain model to compute the average run length and average time to signal values. We conduct extensive numerical analyses to measure the performance of the proposed scheme in two scenarios of process variability. At last, we present a numerical example by using a real dataset from a healthcare process to illustrate how the scheme can be implemented in practice. [ABSTRACT FROM AUTHOR]

Clustered bivariate survival data arise in various fields, such as biology and medicine, when individuals in a dataset are clustered and exhibit two survival outcomes. Recently, the joint frailty-copula model was proposed to analyze clustered bivariate survival outcomes by accommodating the between-cluster heterogeneity via a shared frailty term. In this model, researchers fitted the baseline hazard functions via the nonparametric model, the spline model, or the Weibull model. However, when a population has extremely large survival time, the baseline hazard functions are better modeled by a heavy-tailed distribution. In this paper, we adopt the Pareto type I distribution for the joint frailty-copula model, which is one of the most popular heavy-tailed distributions. We show that the moments of the Pareto type I joint frailty copula model diverge to infinity owing to the heavy right-tail. We develop statistical inference methods based on three types of censoring schemes: (i) bivariate random censoring, (ii) semi-competing risks, and (iii) competing risks. We develop maximum likelihood estimation procedures, and make our computational tools available for users. Simulations are performed to check the accuracy of the proposed method. We finally analyze a real dataset for illustration. [ABSTRACT FROM AUTHOR]