Abstract In this paper, robust Bayesian estimators of error variance in a normal linear model with uncertain hierarchical prior information are investigated. The posterior regret gamma minimax estimator, the least sensitive estimator and conditional gamma minimax estimator for error variance are obtained under two different classes of priors, respectively. A simulation study is used to compare the

Abstract Much of the blame for failed attempts to replicate reports of scientific findings has been placed on ubiquitous and persistent misinterpretations of the p value. An increasingly popular solution is to transform a two-sided p value to a lower bound on a Bayes factor. Another solution is to interpret a one-sided p value as an approximate posterior probability. Combining the two solutions results

Abstract Categorical scale data are only ordinal and defined on a finite set. Continuous scale data are only ordinal and defined on a bounded interval. Due to that character, the statistical methods for scale data ought to be based on orders between outcomes only and not any metric involving distance measure. For simple two-sample scale data, variants of classical rank methods are suitable. For regression

Abstract The Exchange Market Pressure Index (EMPI) is an indicator of pressure on a currency. Because of the presence of serial correlation, financial time series may not be normally distributed even for large sample sizes. They may have undefined parameters and hence parametric tests of normality may give misleading results. In this paper, we look at the time series of EMPI of eleven countries of

Abstract Exit times of diffusion processes play an important role in the application of finance, insurance, biology, engineering, and so on. This article investigates the two-side exit time problems for the Vasicek model. By using Strong Markov property, the Laplace–Stieltjes transform (LST) of some exit times are obtained. And then the results are used to figure out the probability and mathematical

Abstract Localization of quantum Bernoulli noises(LQBNs) are the family of local annihilation and local creation operator acting on Bernoulli functionals. In this paper, we give the local quantum mutual entropy I(ρk;Λ*) based on the local quantum entropy S(ρk). Furthermore, we demonstrate that this quantum mutual entropy I(ρk;Λ*) also has the basic properties.

Abstract In this article, a new two-type parameter estimator is introduced. This estimator is an extension of the two-parameter (TP) estimator presented by Özkale and Kaçiranlar (2007 Özkale, M. R., and S. Kaçiranlar. 2007. The restricted and unrestricted two-parameter estimator. Communications in Statistics - Theory and Methods 36 (15):2707–25. doi: 10.1080/03610920701386877.[Taylor & Francis Online]

Abstract This study examined cyclic non linear structural equation models (SEMs) with an unobserved confounder. The determination of causal direction, identifying whether X causes Y, Y causes X, or X and Y affect each other, is a fundamental issue in science and technology. Unobserved confounding factors are so-called third variables which influence both X and Y. Inclusion of unobserved confounding

Abstract The object of study is the problem of testing for uniformity of the multinomial distribution. We consider tests based on symmetric statistics, defined as the sum of some function of cell-frequencies. Mainly, attention is focused on the class of power divergence statistics, in particular, on the chi-square and log-likelihood ratio statistics. The main issue of the article is to study the asymptotic

Abstract Correlated categorical data often arise from studies involving cluster randomized trials, a cluster sampling scheme, or repeated measurements. The intra-cluster correlation coefficient (ICC) is used to estimate the average correlation within clusters. There have been numerous methods proposed to estimate ICC for correlated binary data, the ANOVA method for continuous data, and several methods

Abstract In this paper, we investigate the lifetime reliability of a system under a new mixed shock model. Consider a system whose efficiency is k. If the magnitude of the shock is greater than d or the interarrival time between two consecutive shocks is less than δ, the efficiency of the system reduces by one unit. If k1 denotes the number of shocks that have the magnitude greater than d and k2 demonstrates

Abstract Regression calibration estimation procedure is proposed in linear errors-in-variables regression model when the measurement error follows a normal distribution. The improvement is made feasible by the Tweedie’s formula. Large sample properties, including the weak consistency and the asymptotic normality are established under some mild conditions. Simulation studies are conducted to evaluate

Abstract A new mixture autoregressive model based on Student’s t–distribution is proposed. A key feature of our model is that the conditional t–distributions of the component models are based on autoregressions that have multivariate t–distributions as their (low-dimensional) stationary distributions. That autoregressions with such stationary distributions exist is not immediate. Our formulation implies

Abstract In this article, we have considered the estimation of the probability density function and cumulative distribution function of the one-parameter polynomial exponential family of distributions. A number of probability distributions like the exponential, Lindley, length-biased Lindley and Sujatha are particular cases. Two estimators—maximum likelihood and uniformly minimum variance unbiased

Abstract Images are often degraded during the data acquisition process. The degradation may involve blurring, information loss due to sampling, and various sources of noise. The purpose of image restoration is to estimate the original image from the degraded data. The present work sets forward a restoration technique for exponential dispersion noise based on Particle filtering (PF) using Hidden Markov

Abstract There are many measures for qualitative and quantitative analysis of ageing phenomena of a system with a well defined statistical distribution, namely, hazard rate, ageing intensity (AI) function etc. The extensive usage of Weibull distributions in various fields has prompted us to explore the ageing property of these models. The present work derives the AI function of recent continuous Weibull

Abstract Change points are abrupt changes in time ordered data. The cumulative sum (CUSUM) test statistic is an important statistic for testing for a change point. In this article, we prove a functional central limit theorem for heterogeneous α-mixing triangular array in D[0,1] assuming a Riemann integrable variance function. We investigate the asymptotic behavior of the CUSUM statistic under the null

Abstract In this article, we compare two parallel systems of heterogeneous-independent Log–Lindley distributed components using the concept of matrix majorization. The comparisons are carried out with respect to the usual stochastic ordering when each component receives a random shock. It is proved that for two parallel systems with a common shape parameter vector, the majorized matrix of the scale

Abstract The test treatment in confirmatory clinical trials is often assessed using multiple primary endpoints. We considered that trial efficacy is confirmed only when there is superiority of at least one endpoint and non-inferiority of the remaining endpoints. Some researchers proposed testing procedures for multiple primary endpoints that are continuous variables. However, there has not yet been

Abstract This study examines a penalized additive regression spline estimator with total variation and non negative garrote-type penalties. The proposed estimator is obtained based on a two-stage procedure. In the first stage, an initial estimator is obtained via total variation penalization. The total variation penalty enables data-adaptive knot selection and regularizes the overall smoothness of

Abstract The choice of a bandwidth can affect dramatically the accuracy of classification methods relying on it. Recently, a large number of methods to choose the bandwidth have been developed. This article presents a simple method called KBER to estimate the bandwidth using the average Ricci curvature of ɛ− graphs. The Radial Basis Function kernel (RBF) has been chosen in our work for its simplicity

Abstract For two vast families of mixture distributions and a given prior, we provide unified representations of posterior and predictive distributions. Model applications presented include bivariate mixtures of Gamma distributions labeled as Kibble-type, non-central Chi-square and F distributions, the distribution of R2 in multiple regression, variance mixture of normal distributions, and mixtures

Abstract q-analogs of special functions, including hypergeometric functions, play a central role in mathematics and have numerous applications in physics. In the theory of probability, q-analogs of various probability distributions have been introduced over the years, including the binomial distribution. Here, I propose a new refinement of the binomial distribution by way of the quantum binomial theorem

Abstract In this paper, we propose a least-squares estimator based on Logistic transformation of order statistics (LLSE) and grouped LLSE for the generalized Logistic distribution. Some asymptotic results are provided. Two simulations are undertaken to assess the performance of the proposed method and to compare them with other methods suggested in this paper. The simulation results indicate that LLSE

Abstract In this paper, we focus on the problem of viability property for the multi-dimensional stochastic differential equations, where the coefficients of the stochastic differential equations may be random and discontinuous in the time variable. First, we establish a necessary and sufficient condition for viability property with respect to a given non-empty closed convex set. And furthermore, with

Abstract Randomized response (RR) technique is an indirect method of data collection for sensitive items. Most RR techniques available in literature are limited to simple random sampling with replacement (SRSWR) method. In this paper the RR technique for multiple sensitive attributes has been provided for complex survey designs. Methods of estimation of population proportions and their variances have

Abstract We propose a semi-parametric method for estimating the multinomial choice model using cyclical monotonicity moment inequalities. In our semiparametric approach, we do not specify the parametric distribution for the utility shocks, thus accommodating a wide variety of substitution patterns among alternatives. Compared with the conditional likelihood estimation method proposed by Chamberlain

Abstract Existing studies on spatial linear mixed models typically assume a normal distribution for the random error components. However, such an assumption may not be appropriate in many applications. This work relaxes the normality assumption of a generalized linear mixed model with spatial correlated by using an unrestricted multivariate skew-normal distribution, which includes the normal distribution

Abstract The characteristic of count data that have a high frequency of zeros and ones can be considered under a zero-one inflated distribution. In this article, we present a zero-one inflated negative binomial - beta exponential distribution to analyze for such data. This distribution shows that it is extended the mixture negative binomial with beta exponential distributions, was proposed by Pudprommarat

Abstract In this paper, we consider stochastic comparisons of parallel systems with location-scale distributed components equipped with starting devices. We specifically establish the hazard rate order of parallel systems with two location-scale distributed components equipped with starting devices when the starting devices have different probabilities but with the same location-scale distributed component

Abstract This paper studies the optimal investment-consumption decision under the constant elasticity of variance (CEV) model for an individual seeking to maximize the expected utility from cumulative consumption plus the expected utility from terminal wealth. Due to the fact that different individuals may have different risk preferences, we assume that the risk preference of an individual satisfies

Abstract The analysis of the product of two normally distributed variables does not seem to follow any known distribution. Fortunately, the moment-generating function is available and we can calculate the statistics of the product distribution: mean, variance, the skewness and kurtosis (excess of kurtosis). In this work, we have considered the role played by the parameters of the two normal distributions’

Abstract Linear mixed models are standard models to analyze repeated measures or longitudinal data under the assumption of normality for random components in the model. Although the mixed models are often used in both frequentist and Bayesian inference, their evaluation from robustness perspective has not received as much attention in Bayesian inference as in frequentist. The aim of this study is to

Abstract The β-wordlength pattern has been justified as an appropriate criterion for measuring designs with quantitative factors. However, construction methods of designs with less β-aberration have not been fully investigated. In this paper, some properties of β-wordlength pattern for three-level designs will be firstly provided, and then a direct construction method is proposed to generate three-level

Abstract In this paper, we introduce and examine the concept of deferred statistical boundedness of order α and give the relation between statistical boundedness and deferred statistical boundedness of order α. Apart from studying the Köthe-Toeplitz duals of Sp,qα(b), the space of deferred statistically bounded sequences of order α, a decomposition theorem is also established. Finally we give a general

Abstract In this paper, we propose nonparametric kernel estimators for Shannon differential entropy function under length-biased sampling. Asymptotic properties of the estimators are established under suitable regularity conditions. A simulation study is accomplished to compare the performance of proposed estimators. The usefulness of the estimators are also examined using a real data.

Abstract In this article, we introduce two new test statistics based on pairwise distance to check whether a parametric model with missing response is correctly specified or not. The proposed test statistics are easy to implement and no non parametric function estimation is involved. The asymptotic properties of the newly introduced test statistics are investigated. Under the null hypothesis, it is

Abstract In this article, we propose a new randomized response model to estimate the population total of a sensitive variable of quantitative nature. The objective is achieved by introducing additive scrambling mechanism when sample is drawn through probability proportional to size sampling scheme. The performance evaluation of the proposed model is carried with respect to notable model of Odumade

Abstract This study endeavors to compare two parallel systems delineated via exponentiated half logistic-F distributions with both identical (F) and non-identical (F1 and F2) baseline distribution functions. The comparisons are carried out with respect to the usual stochastic order as well as the reversed hazard rate order through the majorized shape parameters of the distributions.

Abstract Multi-collinearity among regressors and consequently ill-conditioning inflates the mean squared error (MSE) of the maximum likelihood estimator (MLE) of the parameters in a regression model. In recent years, the Liu estimator (LE) has been widely used in the literature to improve the regression models. Since in some regression models, the dependent variable follows a double bounded distribution

Abstract In this paper, the optimal estimation at a given point is considered for biased density in theory. A lower bound is first provided for all possible estimators over the local Hölder space. Using wavelet method, a linear wavelet estimator is constructed and turned out to be optimal by investigating its upper bound of pointwise convergence rate. To get the adaptivity, a nonlinear wavelet estimator

Abstract In this paper, we obtain a new kind of strong law of large numbers in sublinear expectation spaces without the independent or identically distributed assumption. Instead, the strong law of large numbers is based on some restrictions on the sub-linear expectations of the partial sums. As an application, we give an interesting example in which the random variable sequence enjoys our moment restrictions

Abstract When designing repeated measures studies, both the amount and the pattern of missing outcome data can affect power. The chance that an observation is missing may vary across measurements, and missingness may be correlated across measurements. For example, in a physiotherapy study of patients with Parkinson’s disease, increasing intermittent dropout over time yielded missing measurements of

Abstract For high-dimensional statistical inference, de-sparsifying methods have received popularity thanks to their appealing asymptotic properties. Existing results show that aforementioned methods share the same order of o(1) for the secondary bias term in probability. In this paper, we propose the de-sparsifying hard thresholded estimator (DATE) to further reduce the order. More specifically, we

Abstract The modified Cholesky decomposition (MCD) is a powerful and efficient tool for the large covariance matrix estimation, which guarantees the positive definite property of the estimated matrix. However, when implementing the MCD, it requires a pre-knowledge of the variable ordering, which is often unknown before analysis or does not exist for some real data. In this work, we propose a positive

Abstract The group testing procedure divides sampled units into several groups, and then obtains an overall test result for each group. It is used to identify specific individuals who have a given attribute, or to estimate the overall prevalence of the attribute in the population. We here investigate how group retesting can improve precision of estimation and its cost-efficiency, which are important

Abstract The mixed variable discriminant analysis procedure assumes that observations are distributed multivariate normal with different group means but same variance-covariance matrix. However, attention has not been given in discriminant analysis when the assumption of normality no longer holds. Therefore, we present a simple but new approach to mixed variable discriminant analysis when available

Abstract Uncertain time series analysis is a methodology that deals with expert’s experimental time series data. Previous studies mainly focus on linear models such as an uncertain autoregressive (UAR) model. Nevertheless, the laws of motion in the real world are usually non linear. In order to model the observations that periodically vary over time, this article introduces an uncertain threshold autoregressive

Abstract We consider the Cox regression model and show that the regression parameter estimator and the Breslow estimator for the cumulative hazard have uniformly bounded moments of any order if we restrict to a sequence of events with probability converging to one. These results are needed, for example, when studying global errors of shape restricted estimators of the baseline hazard function.

(2021). Preface. Communications in Statistics - Theory and Methods: Vol. 50, 11th- International Statistics Days Conference, pp. 1531-1531.

Abstract In this paper, we study the problem of excess-of-loss reinsurance and investment for an insurer who wishes to maximize the expected exponential utility of the terminal wealth. The surplus process of the insurer is described by a Brownian motion with drift, while the claim arrival process, the insurance and reinsurance premiums are affected by a stochastic factor. It is also assumed that the

Abstract The approximation properties of finite mixtures of location-scale distributions on Euclidean space have been well studied. It has been shown that mixtures of location-scale distributions can approximate arbitrary probability density function up to any desired level of accuracy provided the number of mixture components is sufficiently large. However, analogous results are not available for

Abstract Suppose we have two sets of exponential random variables with the first set having a common hazard rate and the second having different hazard rate parameters. In this work, we then discuss star, convex transform, right spread and dispersive orders between these two sets of random variables. The results enable us to compare sample spacings in terms of dispersion and variability orders. We

Abstract In this paper, we consider a special class of dependent random variables (APND) that contains negative dependent random variables classes(ND,PND,NUOD,NA,NLOD,) and some classes of positive dependent random variables. Then we generalize Kolmogrov–Feller weak law of large numbers for i.i.d. random variables to APND random variables. we further give corresponding forms of dependence for random

Abstract In this paper, we consider discrete time approximations for stochastic differential equations with the form: Xt=X0+∫0tf(Xs)dhs+∫0tg(Xs)dYsH,  t>0, where h:R+→R is a continuous function with locally bounded variation, f,g:R→R are measurable functions, and the integral with respect to YtH=∫0tσsdSsH is the pathwise Riemann-Stieltjes integral, SH is a subfractional Brownian motion with H∈(12,1)

Abstract To inference the reliability of product at normal stress conditions, accelerated life test (ALT) is usually used to obtain failure information rapidly. However, most of the researches on ALT are focused on the statistical inference with single stress, which makes it difficult to gain accurate reliability through applying ALT method in single stress case. In this article, statistical inference

Abstract In 1971, Chow and Teicher presented a probability approximation Theorem via summability methods. The goal of this article is to extend Chow and Teicher results to higher dimension. To achieve this we consider multidimensional totally monotonic and independent identically random variables. Using these notions we present a series of approximation type theorems.

Abstract Change point detection has been widely used in quality control, earthquake disaster prediction and other fields. Existing change-point analysis methods rarely take into account the computational complexity, memory requirements and privacy issues under large data size. In this paper, we propose a distributed fast algorithm for change-point estimation when data are divided into many computers

Abstract In this paper, we consider an extension of the generalized class of recursive regression estimators to the case of strong mixing data. Then, we study the properties of these estimators and compare them with the well known Nadaraya-Watson estimator. The Bias, variance and Mean Integrated Square Error are computed explicitly. Using a selected bandwidth and a special stepsize, we showed that

Abstract Here we present a new non-parametric approach to density estimation and classification derived from theory in Radon transforms and image reconstruction. We start by constructing a “forward problem” in which the unknown density is mapped to a set of one dimensional empirical distribution functions computed from the raw input data. Interpreting this mapping in terms of Radon-type projections