This paper considers the optimization problems for a consecutive-2-out-of-n:G system where n is considered to be fixed or random. When the number of components is constant, the optimal number of components and the optimal replacement time are discussed by minimizing the expected cost rates. Furthermore, we focus on the above discussions again when n is a random variable. We give an approximate value

In this paper, we propose a new two-stage unrelated question randomized response technique (RRT) model to estimate the mean of the number of persons possessing a rare sensitive attribute using the Poisson distribution. The utility of proposed two-stage unrelated question RRT model under stratification is also explored. Efficiency comparison between proposed two-stage unrelated question and Singh and

This article investigates the issue of stochastic comparison of multi-active redundancies at component level versus system level. In the case of matching and non matching spares, we present some interesting comparison results of coherent systems with dependent heterogeneous components in the sense of the usual stochastic ordering, the hazard rate ordering, and the reversed hazard rate ordering. Several

By using the matrix formulation of the two-step approach to distributions of patterns in random sequences, recurrence and explicit formulas for the generating functions of successions in random permutations of arbitrary multisets are derived. Explicit formulas for the mean and variance are also obtained.

This paper is concerned with the robust feature screening method for ultra-high dimensional right censored data. A new robust and model-free feature screening approach is built upon a screening index constructed from a fresh measure of dependence between the survival time and a single covariate. One attractive property of this newly introduced index is that it equals zero if the survival time and covariate

In this article, we focus on the variable selection for partially varying coefficient model under high dimensional data. Variable selection is proposed based on modal regression estimation with bridge method. Using the B-spline basic function to approximate the non parametric function, a penalty estimation objective equation is constructed. It establishes and proves that the variable selection methods

A multi-objective optimization method for the accelerated degradation test based on Wiener process is proposed in this article in order to solve the problem that a single objective optimization cannot solve the difficulty or even conflicting test configurations caused by different optimization objective functions. An accelerated degradation model is established based on Wiener process, and the unknown

A Stein operator for the runs is derived as a perturbation of an operator for discrete Gibbs measure. Due to this fact, using perturbation technique, the approximation results for runs arising from identical and non-identical Bernoulli trials are derived via Stein’s method. The bounds obtained are new and their importance is demonstrated through an interesting application.

The censored exponential regression model is commonly used for modeling lifetime data. In this paper, we derive a simple matrix formula for the second-order covariance matrix of the maximum likelihood estimators in this class of regression models. The general matrix formula covers many types of censoring commonly encountered in practice. Also, the formula only involves simple operations on matrices

We derive a representation for dynamic capital allocation when the underlying asset price process includes extreme random price movements. Moreover, we consider the representation of dynamic risk measures defined under Backward Stochastic Differential Equations (BSDE) with generators that grow quadratic-exponentially in the control variables. Dynamic capital allocation is derived from the differentiability

A non parametric Shewhart-type control chart based on a partially rank-ordered set (PROS) sampling design is considered in this study to monitor the process mean. Four non parametric estimators are proposed for the variance of PROS sample mean; also, the performances of these estimators are discussed theoretically and numerically. Then, three non parametric PROS control charts are proposed including

Performance of any control scheme in Phase II depends directly on the quality of estimators utilized in Phase I. In practice, outliers could be present in the data which would impact the performance of estimators adversely. This study deals with robust parameter estimation and monitoring linear profiles in the presence of outliers and compares the results with the least squares (LS) estimators. For

The modified Box-Meyer method (MBMM) has been proposed to identify active factors in unreplicated screening experiments. This paper aims to introduce the MBMM into the analysis of screening experiments with lifetime data. Experiments both with and without replicates are considered. Censored observations arise commonly in lifetime data which increases computational complexity when applying the MBMM

In this paper, we investigate an optimal investment problem under two value-at-risk (VaR) constraints faced by a defined contribution (DC) pension fund manager. We apply a concavification technique and a Lagrange dual method to solve the problem and derive the closed-form representations of the optimal wealth and portfolio processes in terms of the state price density. Theoretical and numerical results

Let {Yi;−∞

Abstract This paper explores multivariate data using principal component analysis (PCA). Traditionally, two different approaches to PCA have been considered, an algebraic descriptive one and a probabilistic one. Here, a third type of PCA approach, lying somewhere between the two traditional approaches, called the fixed effects PCA model, is considered. This model includes mainly geometrical, rather

Lieberman and Phillips (Journal of Time Series Analysis) proposed a stochastic unit root model in which the source of the variation of the autoregressive coefficient is driven by a stationary process. More recently, Lieberman and Phillips (Journal of Econometrics) generalized this model to the multivariate case and a hybrid case. Their studies revealed that these stochastic unit root models lead to

Pareto distributions are useful for modeling the loss data in many fields such as actuarial science, economics, insurance, hydrology and reliability theory. In this paper, we consider the simultaneous estimation of the risk parameters of Pareto distributions from the perspective of empirical Bayes, novel SURE-type shrinkage estimators are developed by employing the Stein’s unbiased estimate of risk

(2020). A report on the paper “Sungsu Kim. 2019. The probable error in the hypothesis test of normal means using a small sample. Communications in Statistics - Theory and Methods. DOI: 10.1080/03610926.2019.1703135.”. Communications in Statistics - Theory and Methods. Ahead of Print.

In this work, we extend to the case of the strong mixing data the results of Khardani and Semmar. A kernel-type recursive estimator of the conditional density function is introduced. We study the properties of these estimators and compare them with Rosemblatt’s nonrecursive estimator. Then, a strong consistency rate as well as the asymptotic distribution of the estimator are established under an α-mixing

In order to modify the restriction that the path of the geometric Brownian motion can never reach zero, we consider an extended degradation model based on geometric Brownian motion. This model incorporates some important stochastic processes, such as geometric Brownian motion and the sinh-Gaussian process. We determine the convergence behavior of the first passage time as the random effect vanishes

Ideally, any statistical inference should be robust to local influences. Although there are simple ways to check about leverage points in independent and linear problems, more complex models require more sophisticated methods. Kullback-Leiber and Bregman divergences were already applied in Bayesian inference to measure the isolated impact of each observation in a model. We extend these ideas to models

In this article, we present the American option pricing procedure based on the binomial tree from an imprecise statistical aspect. Nonparametric Predictive Inference (NPI) is implemented to infer imprecise probabilities of underlying asset movements, reflecting uncertainty while learning from data, which is superior to the constant risk-neutral probability. In a recent article, we applied the NPI method

This article derives the moment functions of the truncated skewed type III generalized logistic (SGL). These are then applied in finance for the development of value at risk (VaR), expected shortfall (ES), and downside risk measures for investment returns and values. The SGL distribution provides and good fit to the empirical distribution of a representative set of long series of financial data. Moreover

The expectation part of a linear model is often presented as a single equation with unknown parameters, and the reader is supposed to know that this is shorthand for a whole family of expectation models (for example, is there interaction or not?). It is helpful to list the whole family of models separately and then represent them on a Hasse diagram. This shows which models are sub-models of others

In this paper, we propose a non parametric M-estimator of the regression function and we investigate its asymptotic properties, when the response variable is subject to both random left truncation and right censoring. In most works, non parametric M-estimation requires the use of an objective function ψ supposed to be bounded. Here the results hold with unbounded objective function. The strong uniform

The default variable-importance measure in random forests, Gini importance, has been shown to suffer from the bias of the underlying Gini-gain splitting criterion. While the alternative permutation importance is generally accepted as a reliable measure of variable importance, it is also computationally demanding and suffers from other shortcomings. We propose a simple solution to the misleading/untrustworthy

The confidence band of functions is complicated by the over-smoothing problem and the residual distribution. In this paper, we use bootstrap and data-sharpening methods to establish a general confidence band. The construction is simple and the band is narrower than existing estimation methods. At the same time, a technique based on quantiles makes the confidence band more controllable and damps down

Across different types of lifetime studies, whether it be in the medical or engineering sciences, the possibility of competing causes of failures needs to be addressed. Typically referred to as competing risks, in this article we consider progressively type-II censored competing risks data when the lifetimes are assumed to come from a linear exponential distribution. We develop likelihood inference

In this paper, the generalized restricted difference-based almost unbiased ridge estimator in partially linear model is presented, when it is supposed that the regression parameters may be restricted to a subspace and compare the proposed estimators in the sense of the quadratic bias and scalar mean squared error criteria. Finally, a simulation study is given to explain the performances of the estimators

The present paper deals with the performance evaluation of an M/M/1 retrial queue with collisions, transmission errors and unreliable server. To the best of our knowledge, there are no works that have dealt with retrial queues by considering all the above-mentioned aspects (collisions, transmission errors and unreliable server). This queue can be used as a mathematical model of several computer systems

Two-tailed asymptotic inferences for the ratio R=p2/p1 of two independent proportions have been well covered in the published literature. However, not very much has been written about one-tailed asymptotic inferences. This paper evaluates 63 different methods for realizing such inferences (hypothesis tests and confidence intervals). In general it is noted that: (a) the one-tailed inferences require

For a linear regression model with two-predictor variables, the effects of the correlation between the two predictors on estimated standardized regression coefficients and R2 have been well studied. However, the role the correlation plays may sometimes be overstated, such that confusion and misconceptions may arise. In this article, we revisit the issue from the perspective of a semipartial correlation

Change point in a panel data refers to the time when a change(s) takes a place in the cross-sections of the panel. This key time helps practitioners to analyze the root cause(s) of the change manifested itself to the process. This paper attempts to introduce a new hybrid approach called Double-CUSUM-Modified EWMA (DCME) which is capable of providing a high sensitivity of detecting the change point

Any data set exhibiting an unequal or highly-skewed distribution between its classes/categories can be regarded as imbalanced data. Due to privacy concern and other technical limitations, imbalanced data distributed across locations/machines cannot be simply combined and stored in a single central location. The commonly used naive averaging estimate may be unstable for imbalanced data. In this paper

A collateralized debt obligation (CDO) is a type of structured asset-backed security. The assets are pooled together and divided into tranches to be sold to investors. Each tranche has a substantially different credit quality and risk level. Jaio and Kaouri (2009), Neammanee and Yonghint (2020 Neammanee, K., and N. Yonghint. 2020. Poisson approximation for call function via Stein-Chen method. Bulletin

Doubly-censored data, which consist of exact and case-1 interval-censored observations, often arise in medical studies, such as HIV/AIDS clinical trials. This article considers nonparametric maximum likelihood estimation (NPMLE) of semiparametric transformation models that encompass the proportional hazards and proportional odds models when data are subject to double censoring. The maximum likelihood

This article studies spurious regression in the multivariate case for any finite number of fractionally integrated variables, stationary or not. We prove that the asymptotic behavior of the estimated coefficients and their t-statistics depend on the degrees of persistence of the regressors and the regressand. Nonsense inference could therefore be drawn when the sum of the degrees of persistence of

A quantile-quantile (Q–Q) plot is derived from a characterization for the multivariate normal distribution and the Shapiro–Wilk’s (1965) S–W statistic. The normal characterization results in some independent spherical distributions. The affine invariance of the S–W statistic and a simple property of spherical distributions are employed to construct the Q–Q plot. Easy simulation of the empirical distribution

Under weighted balanced loss function, we obtain the best linear unbiased estimator of regression coefficient in general Gauss–Markov model and discuss the admissibility of linear estimators of the regression coefficient with respect to an ellipsoidal constraint. We establish necessary and sufficient conditions for the admissibility of the linear estimators Ay( Ay+a) among the class of homogeneous

In this paper, we study empirical likelihood-based inference for longitudinal data with varying-coefficient partially nonlinear model. Based on the orthogonality estimation technology, the QR decomposition is firstly used to separate the nonparametric component in the model. With the quadratic inference functions (QIF), we propose an estimator for the parameter that avoids estimating the nuisance parameter

We analyze the asymptotic properties of nonparametric cross spectral density estimators when the time series process has a degenerate spectrum at the origin in the frequency domain. Degeneracy at the zero frequency caused by over-differencing the series invalidates inferences based on cross spectral methods. We derive the asymptotic mean squared errors of kernel-based cross spectral density estimators

Let (Zn) be a supercritical branching process with immigration (Yn) in a random environment ξ. We are interested in the almost sure (a.s.) convergence rate of the submartingale Wn=ZnΠn to its limit W where (Πn) is an usually used norming sequence. The result about convergence a.s. are as following. Under a moment condition of order p∈(1,2) and limn→∞ log m̂nn=0a.s. where, m̂n=EYn W−Wn=o(e−na) a.s.

In this paper, we propose a scale-scale plot to compare multivariate distributions. These scale-scale plots can be viewed as a multivariate analog of quantile-quantile plots and we illustrate their use as a visualization tool to validate distributional assumptions for multivariate data as well as to compare the distributions of two multivariate samples. We discuss some characterizations of the proposed

(2020). Correction. Communications in Statistics - Theory and Methods. Ahead of Print.

This paper proposes a new efficient composite quantile regression (CQR) estimating function for the semivarying models with longitudinal data, which can incorporate the correlation structure between repeated measures via the Gaussian copula. Because the objective function is non-smooth and non-convex, the induced smoothing method is used to reduce computational burdens. It is proved that the smoothed

Svante Janson presented sharper tail bounds for sum of geometric and exponential variables. In this article, we consider for gamma variables with real number parameters and obtain similar results. As a result, more particular examples of gamma variables like exponential variables and chi-square variables can also be included in this framework.

In prognostic/diagnostic medical research, it is often the goal to identify a biomarker that differentiates between patients with and without a condition, or patients that will have good or poor response to a given treatment. The statistical literature is abundant with methods for evaluating single biomarkers for these purposes. However, in practice, a single biomarker rarely captures all aspects of

This article shows how multivariate elliptically contoured (EC) distributions, parameterized according to the mean vector and covariance matrix, can be built from univariate standard symmetric distributions. The obtained distributions are referred to as moment-parameterized EC (MEC) herein. As a further novelty, the article shows how to polynomially reshape MEC distributions and obtain distributions

This paper studies optimal investment and risk control strategies for an insurer who owns insider information. The insurance risk process is governed by a general jump diffusion process with random parameters and is correlated with the risky asset process in the financial market. We model the inside information by a general random variable related to the insurance risk process and the risky asset process

Testing the hypothesis of zero multiple correlation coefficient is of interest in wide variety of applications including multiple regression analysis. In high-dimensional data, traditional testing procedures to test this hypothesis become practically infeasible due to the singularity of the sample covariance matrix. To deal with this problem, an optimal projection test with a computationally simple

In the case of differential privacy under the Laplace mechanism, the asymptotic properties of parameter estimator have been derived in some special models such as β− model, but under a general noisy mechanism, the results are lacking. In this article, we release the degree sequences of undirected weighted networks under a general noisy mechanism with the discrete Laplace mechanism as a special case

The main purpose of this paper is to obtain the complete moment convergence for widely orthant dependent linear processes with random coefficients in form Xt=∑j=−∞∞Ajεt−j, where {εn,n∈ℤ} is a sequence of stochastically dominated WOD random variables and {An,n∈ℤ} is a sequence of random variables.

Recurrent event data frequently occur in longitudinal studies, and it is often of interest to estimate the effects of covariates on the recurrent event rate. This paper considers a flexible semi-parametric additive-multiplicative transformation mean model for recurrent event data, which includes the multiplicative model and additive transformation model as special cases. The new model is flexible in

This paper presents a new efficient and robust inference method by combing the robust generalized estimating equations and the well-known empirical likelihood method in longitudinal data analysis. Based on a bounded exponential score function and leverage-based weights, robust auxiliary random vectors are constructed to achieve robustness against outliers both in the response and the covariate domains

Consider the multiple hypothesis problem for n independent Poisson processes whose jump size of the intensity function varies with n. The intensity function contains two types of parameters, the jump instant and the shift or scale parameter, which produces the dependence of the statistics. The Bayes multiple procedure is proposed to diminish the effect of the dependence while three other procedures

The density function of the limiting spectral distribution(LSD) of sample covariance matrices is widely used in large scale statistical inference when the sample size and dimension both tend to infinity. However, there are no explicit expressions for the density function generated by vector autoregressive moving average(VARMA) models. For such models whose sample covariance matrices do not have independence

This paper introduces a new test of harmful multicollinearity based on the ratio of the levels of significance of ordinary least squares and generalized ridge regression estimates of the coefficients. Harmful multicollinearity is the degree of multicollinearity that leads to an incorrect statistical inference. The proposed test is based on a rule that an insignificant regressor will not change to a

The relationship between reliability and dependence of components within each element is discussed in complex systems. In the present text, a complex system is composed of n elements and each of its elements has two dependent components. In this setting, dependency among components is a crucial issue, since the reliability and mean residual life (MRL) functions of such systems are affected by its component

Indirect approaches based on minimal path vectors (d-MPs) and/or minimal cut vectors (d-MCs) are reported to be efficient for the reliability evaluation of multistate networks. Given the need to find more efficient evaluation methods for exact reliability, such techniques may still be cumbersome when the size of the network and the states of component are relatively large. Alternatively, computing