(2021). Special issue on Statistical Models and Methods in Reliability for the 11th international conference on mathematical methods in reliability (MMR 2019) Communications in Statistics - Theory and Methods: Vol. 50, The 11th International Conference on Mathematical Methods in Reliability (MMR), pp. 3747-3748.

Abstract In this paper we propose an objective Bayesian method to analyze the accelerated degradation model based on the new Wiener process stated in Ye, Chen, and Shen (Reliab. Eng. Syst. Safe., 2015, 139: 58–67). The Jeffreys prior and reference priors are derived after reparameterization, and the posterior properties under each prior are validated. A Metropolis random walk algorithm is then employed

Abstract In this paper, we present a modified one-stage multiple comparison procedure for exponential location parameters with the control under heteroscedasticity including one-sided and two-sided confidence intervals to improve the coverage probability and average confidence length than the old one. These intervals can be used to identify a subset which includes all no-worse-than-the-control treatments

Abstract The hierarchical Bayes predictor of small area proportions (HBP) under an area level version of generalized linear mixed model with logit link function is widely used in small area estimation for binary variable. However, this predictor does not account for the presence of spatial nonstationarity in the data, i.e., where the parameters associated with the model covariates vary spatially. This

Abstract In this paper, we develop unbiased estimators of the finite population cumulative distribution function (CDF) using two-stage and three-stage cluster sampling. In addition, the ranked-set sampling scheme is also used in the secondary and tertiary sampling frames for further increasing the precision of the CDF estimators. This work is then extended to develop unbiased CDF estimators based on

Abstract We investigate the equilibrium behavioral strategy for a defined contribution (DC) pension plan during the accumulation phase in this paper. We adopt a state-dependent function to describe the risk tolerance attitude of a mean-variance (MV) investor, which is a piecewise linear function of the current wealth level with the reference point being the discounted investment target. Meanwhile,

Abstract In this paper, we investigate some strong limit properties for Markov chains indexed by a class of infinite trees, which are the generalizations of the spherically symmetric tree. We first give the definition of the generalized spherically symmetric tree model, then obtain the strong law of large numbers for Markov chain indexed by such tree. Finally, we establish the Shannon-McMillan theorem

Abstract In this paper we analyze the kth-to-default credit-linked notes (CLN) with counterparty risk by the reduced-form model. We study the structure of the kth-to-default CLN and present a general valuation framework for CLN values and counterparty valuation adjustments (CVA) under the conditional independence assumption. Explicit formulas of the kth-to-default CLN values and their CVAs are obtained

Abstract In the recent review published in 2019, Malinovsky and Albert conjectured analytical formulae of the optimal sample sizes for the modified Dorfman and Sterrett group testing schemes and verified the validity of the formulae numerically within a broad range. However, the authors pointed out that they were unable to give a rigorous proof of the stated conjectures. In this note, we affirm their

Abstract This article studies the Hamming distances and association schemes of orthogonal arrays. We present a general method of constructing mixed schematic saturated orthogonal arrays of strength two produced from saturated symmetric orthogonal arrays by using the expansive replacement method. As applications of the method, we obtain many new mixed schematic saturated orthogonal arrays. Some examples

Abstract Ranked Set Sampling (RSS), introduced by McIntyre, and other related methods, such as Partially Rank-Ordered Set Sampling (PROSS), have shown that inclusion of a ranking mechanism produces estimators with lower variance than their simple random sample (SRS)-based counterparts. Like RSS, PROSS takes only one measurement from each partially ranked-ordered set. We propose a sampling plan called

Abstract This study considers a new aspect of the belief function theory to define a belief set, which is characterized by truth, uncertainty and falsity belief degrees as a 3D vector representation. Then, based on the implication of a belief set, one of the similarity measures (i.e. Cosine, Jaccard and Dice) between two belief sets is defined. Furthermore, the weighted similarity measure of these

Abstract Fused Lasso is one of extensions of Lasso to shrink differences of parameters. We focus on a general form of it called generalized fused Lasso (GFL). The optimization problem for GFL can be came down to that for generalized Lasso and can be solved via a path algorithm for generalized Lasso. Moreover, the path algorithm is implemented via the genlasso package in R. However, the genlasso package

Abstract The logrank test is a well-known nonparametric test which is often used to compare the survival distributions of two samples including right-censored observations, it is also known as the Mantel-Haenszel test. The Gρ family of tests, generalizes the logrank test by using weights assigned to observations. In this paper, we present a switch monotonicity property for the Gρ family of tests, which

Abstract In the article, we exploit the Pearson system of distributions to obtain expressions for the posterior mean and posterior variance in Tweedie’s formula. This has interesting consequences in the study of micro-array data where the interest is uncovering unusual genes. Another application deals with the development of new non-parametric tests for the two sample problems of location and of scale

Abstract Various objective priors have been defined for the common correlation coefficient concerning several bivariate normal populations. In this paper, the proposed approach relies on the asymptotic matching of coverage probabilities corresponding to Bayesian credible intervals considering the corresponding frequentist ones. In the present paper, we focus on several matching criteria including quantile

Abstract Response Surface Designs (RSDs) are widely used in process or product optimization studies to explore the input-response relationship. This paper is an attempt to provide a compilation of theoretical developments in the RSDs, since its inception in early 1950s to 2020. Part I (1951–1999) consists of important reviews on basic concepts and its development, which fueled further development during

Abstract The repetitive sampling scheme is utilized in control charts to enhance their detection ability in process shifts. Their performance is usually evaluated under the assumption that the process parameters are known. In this article, we investigate the performance of the X¯ and S2 charts under repetitive sampling when the process parameters are estimated from a preliminary in-control (Phase I)

Abstract Resolvable incomplete block designs are often used in many asymmetrical and symmetrical factorial experiments. In this article, two new methods of constructions are proposed to obtain resolvable incomplete block designs for asymmetrical and symmetrical factorial experiments. Designs generated using the proposed methods have orthogonal factorial structure and all main effects are estimated

Abstract In the present paper, we investigate the optimal investment strategies for an insurer with the liquid constraint. The insurer’s surplus is modeled by a Lévy process. The insurer can invest in N risky assets and a risk-free asset. However, in reality, the insurer needs to keep partial amount of his wealth as liquid reserves to meet with the management, which is called as the liquid constraint

Abstract Methods for monitoring network in the literature mainly use two approaches. One approach assumes a statistical model generated the network data and monitors the estimated parameters of this statistical model over time. The other approach summarizes a network using centrality measurements and then monitor these values. In this article, we assume zero-inflated Poisson regression as an underlying

Abstract In practical problems connected with forecasting, it sometimes happens that the classical regression estimation is not informative enough to make good predictions of a response variable. This occurs typically when multi-modality, asymmetry, or heteroscedastic noise characterizes the underlying distribution function. In this situation, conditional mode estimation may constitute an alternative

Abstract We consider a simple estimator of the density mode using the frequency polygon estimate. We investigate strong consistency of the estimator for strong mixing sequence of real variables under mild assumptions. We study the almost sure rate of convergence and we show that the estimator can achieve optimal almost sure rates of convergence for appropriate choices of the bin widths. The asymptotic

Abstract For a random sample of n iid p-dimensional vectors, each partitioned into b sub-vectors of dimensions pi, i=1,…,b, tests for zero correlation of sub-vectors are presented when pi≫n and the distribution need not be normal. The test statistics are composed of U-statistics based estimators of the Frobenius norm measuring the distance between the null and alternative hypotheses. Asymptotic distributions

Abstract Suppose Vν is the pseudo-variance function of the Cauchy–Stieltjes Kernel family K−(ν) generated by a non degenerate probability measure ν on the positive real line. We determine explicitly the law of large numbers μ for free multiplicative convolution given by Haagerup and Möller in terms of the pseudo-variance function Vν. Some examples of calculations of μ are given for probability measures

Abstract We focus on the development of diagnostic tools and an R package called MNB for a multivariate negative binomial (MNB) regression model for detecting atypical and influential subjects. The MNB model is deduced from a Poisson mixed model in which the random intercept follows the generalized log-gamma (GLG) distribution. The MNB model for correlated count data leads to an MNB regression model

Abstract Missing data often complicates survey practitioners to construct reliable estimates of the required population parameters. Remembering this fact and motivated with the recent work, this article deals with some imputation methods to handle the missing data problem at the beginning of the analysis and some estimation procedures of the current population mean have been proposed in two-occasion

Abstract In this paper the influence measures for the Negative Binomial regression model are presented. Based on the conditional expectation of the complete-data log-likelihood function we derive some influence measures, such as case deletion (global influence) and local influence analysis. For the implementation of the influence measures we present explicit expressions and discuss an appropriate perturbation

Abstract This article considers a bidimensional continuous-time renewal risk model with a constant interest force, in which the claim sizes from the same business line are dependent following a general dependence structure proposed by Ko and Tang (2008 Ko, B., and Q. Tang. 2008. Sums of dependent nonnegative random variables with subexponential tail. Journal of Applied Probability 45:5–95.[Crossref]

Abstract This paper considers wavelet estimations of a multivariate density function based on stratified size-biased and strong mixing data. We provide upper bounds of the mean integrated squared error for linear and nonlinear wavelet estimators in Besov space Bp,qs(Rd). It is shown that the linear estimator achieves the optimal convergence rate in the case of p≥2. Moreover, the convergence rate of

Abstract Process capability indices such as Cp, CpL, CpU, and Cpk have been used for evaluating the performance of a manufacturing process in statistical quality control and statistical process control fields. In this paper, a Bayes estimator of Cpk is constructed such that the prior mean is set to be equal to a specified value while the prior distribution is weakly informative. This estimator is compared

Abstract In this paper, we present a double exponential jump-diffusion option pricing model with stochastic interest rates, stochastic volatility, and stochastic jump intensity. In addition, Markov regime-switching is introduced to modulate the mean-reverting level of the squared volatility. We obtain the analytical pricing formulae for European options under this model. Finally, we use numerical examples

Abstract Kageyama (1972 Kageyama, S. 1972. A survey of resolvable solutions of balanced incomplete block designs. International Statistical Review 40 (3):269–73. doi: 10.2307/1402466.[Crossref], [Web of Science ®] , [Google Scholar]) presented a survey of resolvable solutions of balanced incomplete block designs. Clatworthy (1973 Clatworthy, W. H. 1973. Tables of two–associate–class partially balanced

Abstract A joint conditional likelihood (JCL) method, which is a semiparametric approach, is proposed to estimate the parameters of a logistic regression model when two covariate vectors are missing separately or simultaneously. The proposed method uses one validation and three non validations data sets; it is an extension of the method of Wang et al. who studied the case of one covariate missing at

Abstract This paper aims to study a new stochastic order based upon discrete Laplace transforms. By this order, in a setup where the sample size is random, having discrete delta and nabla distributions, we obtain some ordering results involving ordinary and fractional order statistics. Some applications in frailty models and reliability are presented as well.

Abstract We propose an estimation method, named functional average variance estimation (FAVE), for estimating the EDR space in functional semiparametric regression model, based on kernel estimates of density and regression. Consistency results are then established for the estimator of the interest operator, and for the directions of EDR space. A simulation study that shows that the proposed approach

Abstract In Holm and Alouini (2004 Holm, H., and M. Alouini. 2004. Sum and difference of two squared correlated Nakagami variates in connection with the Mckay distribution. IEEE Transactions on Communications 52 (8):1367–76. doi:10.1109/TCOMM.2004.833019.[Crossref], [Web of Science ®] , [Google Scholar]), an explicit formula for the probability density function of λ1−1Zr+λ2−1Z˜r was obtained, where

Abstract The current investigation considers the query of assessment of estimators of population mean through calibration technique. We proposed new multi-variable calibrated estimator of mean in stratified sampling by employing the g multiple auxiliary variables. We introduce new variance function of the study variable in replacement to chi-square distance function under the assumption of known population

Abstract In this paper, we make use of meta-elliptical copula functions to build a new multivariate distribution with fixed marginal distributions and dependence structure to analyze bounded data. Specifically, we present a flexible p-elliptical multivariate probability distribution in the hypercube (0,1)p p with fixed marginal GF-quantile distributions. We then present some illustrative examples and

Abstract The essence of this paper is to propose some efficient combined and separate classes of estimators for estimating population mean Y¯ under stratified simple random sampling. The bias and mean square error of the proposed classes of estimators are obtained. The proposed estimators are theoretically justified over the conventional mean estimator, classical ratio and regression estimators, Kadilar

Abstract We consider balanced one-way, two-way, and three-way ANOVA models to test the hypothesis that the fixed factor A has no effect. The other factors are fixed or random. We determine the noncentrality parameter for the exact F-test, describe its minimal value by a sharp lower bound, and thus we can guarantee the worst-case power for the F-test. These results allow us to compute the minimal sample

Abstract We introduce a new family of probability distributions that we call the Modified-Half-Normal distributions. It is supported on the positive part of the real line with its probability density proportional to the function x↦xα−1 exp (−βx2+γx)I(x>0),α>0,β>0,γ∈R. We explore a number of its properties including showing the fact that the normalizing constant and moments of the distribution can be

Abstract The problem of sequentially estimating quantiles is considered in the case when the observations become available at random times. Certain class of sequential estimation procedures which are composed of optimal stopping time and sequential minimum risk invariant estimator of a median is obtained under a invariant loss function and with the observation cost determined by a convex function of

Abstract Point prediction of future record values from a sequence of independent and identically distributed Pareto and Lomax random variables is addressed. The focus is on likelihood-based prediction techniques; in particular, the maximum likelihood as well as the maximum observed likelihood prediction principles are invoked to derive predictors. Pitman closeness criterion is used for comparing the

Abstract Categorical variables cannot be handled directly by logistic regression. Rather, they must be encoded or converted into continuous variables. Numerous category encodings have been proposed and used in logistic regression. However, these encodings haven’t been studied analytically. In this paper, we study analytical properties of eight commonly used category encodings in logistic regression

Abstract System signatures have transitioned from an emerging topic to a growing research area. It has become essential to classify different research directions and examine the general trends of this promising research area. This would help in identifying potential research areas requiring future study. In this article, we review the literature on “system signatures,” dating back to 1985, and provide

Abstract In the present work, we discuss the cumulative residual entropy of equilibrium distribution of order n. The work provides a generalization of cumulative residual entropy and its dynamic version and also acts as the entropy of a hierarchy of weighted distributions. We provide a comparison of the new entropy with the corresponding Shannon’s entropy and discuss their properties.

Abstract Presence of one or more outliers in the observations affect inference procedure in statistical analysis. Designs robust against presence of a single outlier can be found in the literature for both regression and block design set-ups. In this paper, an attempt has been made to find a robust design in a block design set-up for the estimation of a full set of orthonormal treatment contrasts when

Abstract The purpose of this article is to determine and construct ϕ-optimal designs over the class of all circular cross-over designs with two treatments when the number of both periods and experimental subjects is even. We are interested in estimating the contrasts of both direct and carry-over effects jointly, and minimizing the variances of the best linear unbiased estimators of contrasts of direct

Abstract This work sets the matrix variate Birnbaum–Saunders theory in the context of singular distributions and elliptical models. The termed singular matrix variate generalized Birnbaum–Saunders distribution is obtained with respect the Hausdorff measure. Several basic properties and particular cases of this distribution are also derived.

Abstract In this paper, a new class of location-invariant semi-parametric estimators of a positive extreme value index γ>0 is proposed. Its asymptotic distributional representation and asymptotic normality are derived, and the optimal choice of the sample fraction by mean squared error is also discussed for some special cases. Finally comparison studies are provided for some familiar models by Monte

Abstract In social and behavioral surveys, researchers often have interest in obtaining separate estimates for the parameters of the study variable in specific domains, categorized according to some attribute(s) such as political affiliation, income status, residency, and ethnical affiliations etc. When complete information about such attributes are not available in advance, surveyors need to include

Abstract Missing data can hardly be prevented in most experiments due to setbacks that occur during the data entry process, and may grossly affect the estimation of the regression coefficients. The effects of missing data may be extremely significant if the design is almost saturated, saturated or fully saturated. It is of practical significance to identify designs that are least affected by missing

Abstract In this paper, we apply the profile least-square method and inverse probability weighted method to define estimation of the error variance in partially linear varying-coefficient model when the covariates are missing at random. At the same time, we construct a jackknife estimator and jackknife empirical likelihood (JEL) statistic of the error variance, respectively. It is proved that the proposed

Abstract Countries use either the Dutot, Carli or Jevons indices for the calculation of their Consumer Price Index (CPI) at the lowest level of aggregation. In this paper, we compare expected values and variances of sample elementary indices under the assumption that prices are described by a geometric Brownian motion (GBM). We consider two situations, i.e., the case with only one homogeneous product

Abstract Two primary concerns of inference for high-dimensional data are statistical accuracy and computational efficiency. Despite the appealing asymptotic properties of existing de-biasing methods, the de-biasing step is generally considered to be computationally intensive. In this article, we propose the constrained projection estimator (CPE) for deriving confidence intervals in a scalable and efficient

Abstract The spatial random effects model is popular in analyzing spatially referenced data sets. The model includes spatially observed covariates and unobserved spatial random effects. If spatial confounding between covariates and random effects is ignored, parameter estimation and spatial prediction would be inaccurate. In this research, we focus on discussing the estimation of regression coefficients

Abstract The exponential weighted moving average (EWMA) statistic is utilized the past information along with the present to enhance the efficiency of the estimators used for estimating the population parameters. In this study, the EWMA statistic is used for the estimation of population mean with suitable auxiliary information. The memory type ratio and product estimators are proposed under ranked-based

Abstract In this paper, we mainly focus on the valuation for the risk-based premium of private pension plan with termination provided by the Pension Benefit Guaranty Corporation (PBGC). The dynamics for assets of both the pension fund and the sponsoring company are described by jump diffusion processes. We obtain the pricing formula for the risk-based premium with premature termination and analyze

Abstract The accelerated failure time model is an alternative method to deal with survival data if the proportional hazard model fails to capture the relationship between the hazard time and covariates. That is, the proportionality assumption is not suitable to analyze survival data. In this paper, we address the issue that the relationship between the hazard time and the main effect with unrecognized