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The purpose of this note is to point out a problem related to stress-strength models in some published papers. This difficulty has occurred in the asymptotic variance of the maximum likelihood estimator of the stress-strength parameter. The asymptotic variance will be studied in general and then in the mentioned papers. Finally, the correct version of asymptotic variance is computed. [ABSTRACT FROM AUTHOR]

This document is a letter to the editor addressing a typographical error in the formulas for the double Pareto-lognormal distribution and the normal-Laplace distribution. The authors clarify that the formulas themselves are correct, but there was an error in the expression of the Mills ratio in the correction by Amini and Rabbani. The authors provide the correct formulas for both distributions and offer further explanation upon request. The authors are affiliated with Juraj Dobrila University of Pula in Croatia. [Extracted from the article]

Note, for instance, that the probabilities given by Castellares et al. ([1]) in page 4 are the same than those shown in expression (9.115) in the book by Johnson et al. ([3]), with the change of parameters Graph HT ht and Graph HT ht Neyman type A (NTA) distribution is frequently used in Biology, Biodosimetry, Environmental Sciences, Epidemiology, etc. A count random variable I X i is said to follow a stopped-sum Poisson, compound Poisson, multiple Poisson or clustered-Poisson distribution, if it can be represented as Graph HT ht where I N i is a Poisson random variable with parameter Graph HT ht and Graph HT ht are independent, identically distributed random variables that are also independent of I N i . [Extracted from the article]

This paper presents a flexible family of 2- and 3-parameter distributions whose support is the closed interval [0,1], with explicit density, cumulative density, and quantile functions. These distributions are suited to modeling quantiles, thereby expanding the toolbox of distributions for doubly-bounded random variables. The densities at the boundaries are determined by dispersion and skew parameters, and a third parameter exclusively influences location. The paper also discusses practical issues of parameter estimation and assesses estimation bias, Type I error-rate accuracy, and parameter-estimate collinearity. It also provides three examples of applications to real data using new packages implementing the distributions in R and Stata. [ABSTRACT FROM AUTHOR]

AbstractThis paper investigates a scheduling imperfect maintenance policy for an operating system that works at random times for multiple jobs (n tandem jobs or n parallel jobs). We consider the system suffers from type-I failure which is corrected by a minimal repair, or type-II failure, which is disaster and is eliminated by a corrective maintenance. To control the deterioration process, preventive maintenance is design to go through at a scheduling time T or the completion of multiple jobs, whichever occurs last. Each maintenance is performed imperfectly, the system improves yet its failure characteristic is also changed after maintenance. Lastly, the system is displaced at the N-th maintenance. On the basis minimizes the mean cost rate, this paper derived the optimal scheduling parameters (T*, n*, N*) analytically and numerically, according to its existence and uniqueness. The models we proposed will provide a general structure for maintenance theory of reliability. [ABSTRACT FROM AUTHOR]

As the most widely-used data form in the field of finance, the open-high-low-close (OHLC) data is being collected by all kinds of financial trading systems all the time. This paper puts forward a pseudo-principal component analysis (PCA) for multi-dimensional OHLC data, which can extract their useful information in a comprehensible way for visualization and easy interpretation. Firstly, a novel feature-based representation for OHLC data is proposed, which contains fruitful and explicit economic implications. Next, we define a full set of numerical characteristics and variance-covariance structures for the feature-based OHLC data. Then, the pseudo-PCA procedure for OHLC data is deduced based on the proposed algebraic operators. Finally, the effectiveness and interpretability of the proposed pseudo-PCA method are verified through finite simulations and three typical empirical experiments. This paper enriches the application scenarios of classical PCA and contributes to the multivariate statistical modeling of symbolic data. The proposed applications can serve as models for related studies. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of strongly generalized convex functions which is called as strongly η-convex stochastic processes. We prove the Hermite-Hadamard, Ostrowski type inequality, and obtain some important inequalities for above processes. Some previous results are special cases of the results obtained in this paper. [ABSTRACT FROM AUTHOR]

In this paper, we propose to consider the dependence structure of the trade/no trade categorical sequence of individual illiquid stocks returns. The framework considered here is wide as constant and time-varying zero returns probability are allowed. The ability of our approach in highlighting illiquid stock's features is underlined for a variety of situations. More specifically, we show that long-run effects for the trade/no trade categorical sequence may be spuriously detected in presence of a non-constant zero returns probability. Monte Carlo experiments, and the analysis of stocks taken from the Chilean financial market, illustrate the usefulness of the tools developed in the paper. [ABSTRACT FROM AUTHOR]

This paper focuses on the likelihood ratio test (LRT) statistics for different hypothesis tests. Assuming that a random sample is from a normal population, we make the sample size n and the dimension p close to infinity and satisfy p < n − c for some 1 ≤ c ≤ 4. Based on this assumption, the moderate deviation principle (MDP) for the LRT will be given under the null hypothesis. The corresponding numerical simulation results are shown at the end of the paper. [ABSTRACT FROM AUTHOR]

In this paper, the seven equivalent conditions of complete moment convergence and complete integral convergence for m -asymptotic negatively associated ( m -ANA, for short) random variables are established. The results obtained in the paper extend and improve some corresponding ones for negatively associated (NA, for short) random variables and negatively orthant dependent (NOD, for short) random variables. As an application of our main results, we present a result on complete consistency for the weighted estimator in a nonparametric regression model based on m-ANA errors. We perform a numerical simulation to verify the validity of the theoretical results. [ABSTRACT FROM AUTHOR]

In several papers, conditional variance and left truncated variance have been studied by several authors. Since one of the most important types of systems structures is the parallel structure, in this paper, we obtain conditional covariance and variance of this system consisting of n identical and independent components under the condition that, at time x, all components are still working. Moreover a lower bound for variance residual life is given and furthermore, we check its behavior. Furthermore, as an aplication, we obtain lower bounds for varextropy. Also we obtain varextropy of a parallel system and the results of the varextropy of order statistics are applied to construct a test for symmetry. A real dataset is examined to illustrate the empirical performance of the proposed test statistics. [ABSTRACT FROM AUTHOR]

The redundancy allocation problem is to find an optimal allocation of redundant components by considering the set of resources and cost constraints. In this research, the satellite attitude determination and control system is studied and its components is introduced, then the reliability of this system is modeled and optimized based on a mathematical approach based on the redundancy allocation. The model studied in this paper is about the structure of a series-parallel system that is in the exact mode of a satellite attitude determination and control system. In this paper, a new approach for modeling and optimization is presented. The mathematical model presented in this paper is into the class of mixed integer non-linear programming (MINLP). Solving these problems is very important for various researchers due to the high mathematical complexity. In this research, a heuristic method is used to the problem exact solution, the results of which have been reported. [ABSTRACT FROM AUTHOR]

In this paper we show how a variant of Stone and Brook's continuum regression criterion may be used to define the least variance ratio estimator of the slope parameters of the simultaneous equations model of econometrics. As a by-product of this approach we identify a family of estimators (distinct from the family of k-class estimators) to which it and two variants of the orthogonal least squares estimator belong. We also take the opportunity to mention several features of linear unbiased scalar residuals omitted from an earlier paper. [ABSTRACT FROM AUTHOR]

In this paper, a three components repairable system with K-mixed redundancy strategy is proposed, in which the lifetimes of components, the repair time of failure components and the vacation time are distributed with different phase-type (PH) distributions. The different phases can represent different operational levels, repair levels and vacation levels. The multiple vacation policy is also adopted so that the human resources can be fully utilized. The repairable system is studied in both transient and stationary regimes with the matrix-analytic method, and not only some traditional reliability indexes are obtained, but also several new reliability indexes are obtained by employing Kronecker operator theory and aggregated stochastic theory. Finally, a numerical example is implemented to illustrate the results obtained in the paper. [ABSTRACT FROM AUTHOR]

This paper investigates the power performance of five tests, including improved versions of two existing tests, for jointly testing the equality of origin and scale parameters of two samples from a shifted (two-parameter) exponential distribution. The power of the test varies with a shift in either or both of the two parameters. Therefore, a power surface is observed for various tests. Different tests are optimal for different shift sizes. This paper also compares the volume under the five tests' power surfaces to determine an overall best when the shift size is unknown. The generalized likelihood ratio (GLR) test, the Bayoud and Kittaneh test based on Weitzman's overlapping coefficient, recently designed Max and Distance tests, and an improved likelihood-based procedure are compared. The shifted exponential distribution is often an appropriate probability model for the lifetime of a product with a warranty, high voltage current in specific semiconductor transistors, and military personnel vehicles' mileages that failed in operation. The number of survival days for patients with irreversible lung cancer often follows the same distribution. This distribution plays a vital role in the engineering and biomedical sciences. We observe that the newly designed tests and the exact GLR test are almost always preferable to the other tests. We illustrate the proposed exact test procedures with two practical examples. [ABSTRACT FROM AUTHOR]

In the past few years, considerable attention has been given to the extropy measure. The extropy and weighted extropy of ranked set sampling were studied by several authors. The general weighted extropy and some results related to it are introduced in this paper. We provide general weighted extropy of ranked set sampling. We also studied characterization results, stochastic comparison and monotone properties of general weighted extropy. [ABSTRACT FROM AUTHOR]

Non-additive measures are important for many applications. In this paper we propose an extension of the non-additive measure using the concept of Kerridge inaccuracy and cumulative Tsallis entropy. Several properties including non-linear transformation, bounds and characterizations are obtained using this measure. We also study different properties of the quantile version of the proposed measure. Finally, we numerically illustrate the usefulness of the measure and its quantile form using kernel density estimators. [ABSTRACT FROM AUTHOR]

Recently, providing a new count regression model is very popular for many researchers. These count regression models are constructed by using a new discrete distribution or one of the existing distributions in the literature. In this paper, we consider a new zero-inflated regression model as an alternative to the zero-inflated regression models. We present two real data applications to illustrate the usefulness of the suggested regression model in modeling data, and compare the competitor models such as Poisson, discrete Lindley, and zero-inflated regression models. We provide a new count regression model which is useful in modeling overdispersed data. [ABSTRACT FROM AUTHOR]

In this paper, we extend the result on the probability of (falsely) connecting two distinct components when learning a GGM (Gaussian Graphical Model) by the joint regression based technique. While the classical method of regression based technique learns the neighbours of each node one at a time through a Lasso penalized regression, its joint modification, considered here, learns the neighbours of each node simultaneously through a group Lasso penalized regression. [ABSTRACT FROM AUTHOR]

Mixed-level designs are widely used in various experiments. This paper considers how to construct minimum aberration 4 1 2 n mixed-level designs. Based on finite projective geometry, secondary complementary set is defined as part of the design which plays a crucial role in constructing the optimal designs. Then, algebraic connection between the wordlength pattern of a 4 1 2 n design and that of its secondary complementary set is established. According to the connection, some general rules for identifying type 0 minimum aberration 4 1 2 n mixed-level designs are proposed via their secondary complementary sets. Those rules can help construct minimum aberration 4 1 2 n designs conveniently when the secondary complementary set contains fewer elements than the complementary set. The type 0 minimum aberration 4 1 2 n designs with large n are tabulated via secondary complementary sets. [ABSTRACT FROM AUTHOR]

Bootstrap is a widely applicable computational statistical method. The focus of this paper lies in developing a bootstrap method for linear mixed models under homoscedasticity violation (heteroscedasticity) in variance of errors. We assume that the form of heteroscedasticity is unknown. To generate bootstrap response data as close as possible to the actual response data, we transform the marginal residuals to ensure that the variance of the modified marginal residuals in bootstrap samples is an unbiased estimator for the variance of the response variable in the linear mixed models. The consistency is proved, implying that the parameter estimators by the proposed method are asymptotically unbiased. The simulations are conducted with varying error terms and sample sizes to show improvement of the proposed method in parameter estimation. The simulation results are compared to demonstrate that the proposed method outperforms the other considered approaches including the wild method in the heteroscedastic linear mixed models under small samples and performs competitively with the parametric method and both methods outperform the other considered methods in homoscedastic linear mixed models. The proposed bootstrap method is applied to squid data for illustration of its effectiveness. [ABSTRACT FROM AUTHOR]

The problem of constructing locally D-optimal designs for two-variable logistic model with no interaction has been studied in many literature. In Kabera, Haines, and Ndlovu (2015), the model is restricted to have positive slopes and negative intercept for the assumptions that the probability of response increases with doses for both drugs and that the probability of response is less than 0.5 at zero dose level of both drugs. The design space mainly discussed is the set [ 0 , ∞) × [ 0 , ∞) , while the finite rectangular design space is presented only in scenarios where the results for the unlimited design space are still appropriate. In this paper, we intend to loose these restrictions and discuss the rectangular design spaces for the model where the D-optimal designs can not be obtained. The result can be extended to the models where drugs have negative or opposite effects, or the models with positive intercept, by using translation and reflection in the first quadrant. [ABSTRACT FROM AUTHOR]

We propose a condition which is valid for a class of continuous Gaussian processes that may fail to be self-similar or have stationary increments. Some examples include the sub-fractional Brownian motion and the bi-fractional Brownian motion and the sub-bifractional Brownian motion. Under this assumption, we show an upper bound for the difference between the inner product associated with a class of Gaussian process and that associated with the fractional Brownian motion. This inequality relates a class of Gaussian processes to the well studied fractional Brownian motion, which characterizes their relationship quantitatively. As an application, we obtain the optimal Berry-Esséen bounds for the quadratic variation when H ∈ (0 , 2 3 ] and the upper Berry-Esséen bounds when H ∈ (2 3 , 3 4 ]. As a by-product, we also show the almost sure central limit theorem (ASCLT) for the quadratic variation when H ∈ (0 , 3 4 ]. The results in the present paper extend and improve those in the literature. [ABSTRACT FROM AUTHOR]

The paper treats the modeling of stationary multivariate stochastic processes via frequency domain, and extends the notion of generalized autocovariance function, given by Proietti and Luati (2015) for univariate time series, to the multivariate setting. The generalized autocovariance matrices are defined for stationary multivariate stochastic processes as the Fourier transform of the power transformation of the spectral density matrix. Then we prove the consistency and derive the asymptotic distribution of frequency domain non-parametric estimators of the generalized autocovariance matrices, based on the power transformation of the periodogram matrix. Generalized autocovariance matrices are used to construct white noise hypothesis testing, to discriminate stochastic processes, and to introduce a generalized Yule–Walker estimator for the spectrum. A so-called λ–squared distance between two multivariate stochastic processes is also defined by using their generalized autocovariance matrices, and it serves for clustering time series and estimation by feature matching. Another use is in discriminant analysis. [ABSTRACT FROM AUTHOR]

This paper is concerned with the problem of constructing the locally D-optimal designs for spline measurement error models with estimated knots, where the degree of splines is at most m in each subinterval delimited by knots and it is continuous and differentiable at any knot. Given the number of knots in advance, an equivalence theorem is established and used to check the D-optimality of designs. The characterizations of the locally D-optimal designs are provided under certain conditions. It is shown that the support points of the D-optimal designs for such models are associated with the endpoints of the design interval. The locally D-optimal designs for a class of the models can be determined explicitly. Two examples are presented for illustration. [ABSTRACT FROM AUTHOR]

A random effects model for analyzing mixed rank and binomial data with considering the missing values is presented. Occurring of missing data is an important problem in all research fields. The most common approach to dealing with missing data is to delete cases containing missing observations. However, this approach reduces statistical power and mislead us to biased statistical results. This paper aims to prepare guidance for researchers facing missing data problems and to provide techniques for jointly modeling of binomial and rank responses. We compare the cognitive abilities of different primates based on their performance on 17 cognitive assessments obtained on either a rank or binomial scale using Bayesian latent variable with random effects models. Random effects are used to take into account the correlation between responses of the same individual. [ABSTRACT FROM AUTHOR]

In this paper, we design the Pareto-optimal reinsurance contract for both the insurer and the reinsurer by minimizing the convex combination of the risk-adjusted value of the insurer's liability and the reinsurer's liability, where capital at risk is calculated by the value at risk (VaR) or conditional value at risk (CVaR). In order to prevent the moral hazard, we assume that both ceded and retained loss functions are increasing functions. We analyze the optimal solutions for a wide class of reinsurance premium principles. When the reinsurance premium principles satisfy three axioms: law invariance, risk loading and preserving convex order, we find that layer reinsurance is always optimal over the assumed risk measures. Then we impose an additional weak constraint on the premium principle to simplify the form of layer reinsurance which is optimal. Finally, we illustrate the applicability of our results by deriving the parameters of the optimal layer reinsurance explicitly under the expected value principle and Wang's premium principle. [ABSTRACT FROM AUTHOR]

In this paper, stochastic Gilpin-Ayala model driven by α-stable process under regime switching is presented. Firstly, we prove the existence and uniqueness of the solution for the stochastic model. Then, under certain conditions, the almost sure exponential stability and pth moment exponential stability of the trivial solution are obtained. The results indicated that the α-stable noises can make the trivial solution stable under some conditions. Computer simulations are presented to illustrate our theory. [ABSTRACT FROM AUTHOR]

Estimation of causal treatment effects has attracted a great deal of interest in many areas including social, biological and health science, and for this, instrumental variable (IV) has become a commonly used tool in the presence of unmeasured confounding. In particular, many IV methods have been developed for right-censored time-to-event outcomes. In this paper, we consider a much more complicated situation where one faces interval-censored time-to-event outcomes, which are ubiquitously present in studies with, for example, intermittent follow-up but are challenging to handle in terms of both theory and computation. A sieve maximum likelihood estimation procedure is proposed for estimating complier causal treatment effects under the additive hazards model, and the resulting estimators are shown to be consistent and asymptotically normal. A simulation study is conducted to evaluate the finite sample performance of the proposed approach and suggests that it works well in practice. It is applied to a breast cancer screening study. [ABSTRACT FROM AUTHOR]

In this paper, we consider a risk model with heavy-tailed claims and Brownian perturbation. Assuming that the distribution function of claim-size is subexponential, and the arrival process of claims is a non stationary process satisfying the principle of large deviation, the asymptotic formula for the ruin probability of this risk model at random time is obtained. [ABSTRACT FROM AUTHOR]

In this paper, we prove an extension of the Jajte weak law of large numbers for exchangeable random variables. We make a simulation to illustrate the asymptotic behavior in the sense of convergence in probability for weighted sums of exchangeable weighted random variables. [ABSTRACT FROM AUTHOR]

The notion of weighted Renyi's entropy for truncated random variables has recently been proposed in the information-theoretic literature. In this paper, we introduce a generalized measure of it for double truncated distribution, namely weighted generalized interval entropy (WGIE), and study it in the context of reliability analysis. Several properties, including monotonicity, bounds and uniqueness of WGIE are investigated. Moreover, the proposed measure is estimated using parametric approach and a simulation study is carried out to demonstrate the performance of the estimates for a real data set. The role of WGIE in reliability modeling has been investigated. We also provide an application of the proposed concept in coding theory. [ABSTRACT FROM AUTHOR]

In this paper, we look at the distributions of runs and scans in multistate Markov exchangeable sequences. The joint distributions of runs of several lengths under four types of enumeration schemes are analyzed. We evaluate the upper tail probabilities for ratchet scan statistics exactly. By utilizing the expansion of the generating functions, we propose effective computational tools for the derivation of probability functions. The results presented here provide approaches for the evaluation of the exact distributions of runs and scans in a wide class of practical problems. Finally, we discuss several applications and numerical examples to show how our theoretical results are applied to the investigation of runs and scans, as well as a parameter estimation problem. [ABSTRACT FROM AUTHOR]

Variable selection approaches are often employed in high-dimensionality and multicollinearity problems. Since lasso selects variables by shrinking the coefficients, it has extensive use in many fields. On the other, we may sometime have extra information on the model. In this case, the extra information should be considered in the estimation procedure. In this paper, we propose a stochastic restricted lasso estimator in linear regression model which uses the extra information as stochastic linear restrictions. The estimator is a generalization of mixed estimator with L1 type penalization. We give the coordinate descent algorithm to estimate the coefficient vector of the proposed method and strong rules for the coordinate descent algorithm to discard variables from the model. Also, we propose a method to estimate the tuning parameter. We conduct two real data analyses and simulation studies to compare the new estimator with several estimators including the ridge, lasso and stochastic restricted ridge. The real data analyses and simulation studies show that the new estimator enjoys the automatic variable selection property of the lasso while outperforms standard methods, achieving lower test mean squared error. [ABSTRACT FROM AUTHOR]

In this paper, the longitudinal data analysis is used to interpret the balanced Bühlmann credibility model with correlation risk, and the homogeneous credibility estimator is derived. We obtain the restricted maximum likelihood estimators (RMLE) for the structural parameters involved in the credibility factor and show that they are unbiased. In addition, the linear Bayes method is employed to estimate the structural parameters, and the proposed linear Bayes estimators (LBE) appear to outperform RMLE in terms of the mean squared error matrix (MSEM) criterion. Simulation studies show that the proposed LBE performs well. [ABSTRACT FROM AUTHOR]

As an important result in extreme value theory, Karamata theorem provides the integral properties of regularly varying functions. In this paper, the third-order version of Karamata theorem is derived, which is generalization for the known Karamata theorem. Furthermore, analytic expressions for the second and third-order regularly varying function are established. [ABSTRACT FROM AUTHOR]

The Dickey-Fuller test (DF test) and its various modified versions have been widely used for unit root or random walk testing, though advices are necessary regarding their proper use in hands-on statistical algorithm software. In this paper, we review the development of such tests over several decades. We examine why such modified versions of DF tests were developed and proper instructions regarding their use are essential. In addition, we discuss a simple way to overcome this hurdle. [ABSTRACT FROM AUTHOR]

The asymptotic properties of nonparametric kernel estimators of diffusion process and integrated diffusion process were studied by scholars through using the theories of local time, giving the properties of consistency and asymptotic normality for nonparametric kernel estimators under appropriate conditions, but not property of strong consistency for integrated diffusion process. Instead of using the local time method, the paper applies the moment inequality of the ρ-mixing sequence to prove the strong consistency of the nonparametric kernel estimators in the integrated diffusion process. Our theorem conditions are mild and canonical, and some of them improve on the existing corresponding conditions. In numerical simulations and analysis of data from real applications, the nonparametric kernel estimators can capture well the variation characteristics of drift coefficient and diffusion coefficient, and that it is possible to fit parametric models with such characteristics, so that the economic interpretation of the models can be obtained. [ABSTRACT FROM AUTHOR]

In this paper, we propose a MIXED penalty for the LAD regression model, which can estimate parameters and select important variables efficiently and stably. The proposed method has a good performance in the case of dependent variable with heavy tail and outliers, so this estimator is robust and efficient for tackling the problem of heterogeniety. We show that the proposed estimator possesses the good properties by applying certain assumptions. In the part of numerical simulation, we give several simulation studies to examine the asymptotic results, which shows that the method we proposed behaves better. [ABSTRACT FROM AUTHOR]

This paper studies the optimal reinsurance and investment problem with multiple risky assets and correlation risk. The claim process is described by a Brownian motion with drift. The insurer is allowed to invest in a risk-free asset and multiple risky assets and the instantaneous return rate of each risky asset follows the Ornstein-Uhlenbeck (O-U) model. Moreover, the correlation between risk model and the risky assets' price is taken into account. We first consider the optimal investment problem for the insurer. Subsequently, we assume that the insurer can purchase proportional reinsurance and invest in the financial market. In both cases, the insurer's objective is to maximize the expected exponential utility of the terminal wealth. By applying stochastic control approach, we derive the optimal reinsurance and investment strategies and the corresponding value functions explicitly. Finally, numerical simulations are presented to illustrate the effects of model parameters on the optimal reinsurance and investment strategies. [ABSTRACT FROM AUTHOR]

We consider an exchangeably weighted bootstrap for function-valued estimators defined as a zero point of a function-valued random criterion function. A large number of bootstrap resampling schemes emerge as special cases of our settings. The main ingredient is the use of a differential identity that applies when the random criterion function is linear in terms of the empirical measure. Our results are general and do not require linearity of the statistical model in terms of the unknown parameter. We also consider the semiparametric models extending Zhan's work to a more delicate framework. The theoretical results established in this paper are (or will be) key tools for further developments in the parametric and semiparametric models. [ABSTRACT FROM AUTHOR]

For a model incorporating the effect of a common environment on several components of a system, a multivariate Lomax distribution (MLD) is generally considered by mixing exponential variables. Objective Bayesian has very good frequentist properties and provides a moderate solution for the prior elicitation which is one of important and difficult issues on Bayesian analysis. In this paper, we develop noninformative priors, such as the probability matching priors and reference priors, for the parameters of the MLD. We proved that a reference prior for the shape parameter is a first-order probability matching prior, but the reference priors for the scale parameters do not satisfy the first-order matching criterion. In addition, a second-order probability matching prior does not exist for all parameters. We also presented the conditions that make the posterior distributions for the general prior, including the probability matching prior and reference priors, to be proper. In particular, Jeffreys' prior and probability matching priors for all parameters give proper posteriors, whereas reference priors for scale parameters give improper posteriors. [ABSTRACT FROM AUTHOR]

Let B a , b be a weighted-fractional Brownian motion with Hurst indexes a and b such that a > − 1 and 0 < b < 1 ∧ (1 + a). In this paper, we consider the linear self-repelling diffusion d X t a , b = d B t a , b + (θ ∫ 0 t (X t a , b − X s a , b) ds + ν) dt with X 0 a , b = 0 , where θ > 0 , ν ∈ R are two real parameters. The process is an analogue of the linear self-interacting diffusion (Cranston and Le Jan, Math. Ann.303 (1995), 87-93). We introduce its large time behaviors, and the behavior presents a recursive convergence which is quite different from the asymptotic behavior of stochastic differential equations without interacting drifts. As a related question, we also consider the asymptotic behaviors of the least squares estimations of θ and ν. [ABSTRACT FROM AUTHOR]

The random coefficient autoregressive (RCAR) processes are very useful to model time series in applications. It is commonly observed that the random autoregressive coefficient is assumed to be an independent identically distributed (i.i.d.) random variable sequence. To make the RCAR model more practical, this paper considers a new RCAR(1) model driven by explanatory variable and observations. We use the conditional least squares, the quantile regression and the conditional maximum likelihood methods to estimate the model parameters. The consistency and asymptotic normality of the proposed estimates are established. Simulation studies are conducted for the evaluation of the developed approaches and two applications to real-data examples are provided. The results show that the proposed procedures perform well for the simulations and application. [ABSTRACT FROM AUTHOR]

Confidence intervals Since the I t i test and the test based on the I K i SB 1 sb statistic are the same, the confidence intervals (CIs) that are obtained by inverting these two tests should be the same. Thus, if I t SB q sb i denotes the 100 I q i percentile of the I t i statistic, then Graph HT ht is the 100 I q i percentile of the I K i SB 1 sb statistic. [Extracted from the article]

Recently, multi-regional trials have attracted much attention from sponsors as well as regulatory authorities. For researchers, it is always concerned about how to design a multi-regional trial. The fixed effect model is usually used to design a multi-regional trial. These methods were based on the assumption that true effect size is uniform across regions. However, this assumption is based on no ethnic or environmental factor among regions. In practice, it is necessary to consider the existence of ethnic or environmental factor among regions for a multi-regional trial. The random effect model is employed to deal with the heterogeneous effect size among regions. However, Most papers focus on multi-regional trials for three regions. In this paper, the multi-regional trials by a fixed effect model and a random effect model for four or five regions are designed and evaluated. The design of the multi-regional trials is evaluated by the proposed criteria considering the number of the regions. The assurance probability of proposed criteria considering the number of the regions is employed to determine if the clinical design is suitable for a multi-regional trial. More regions in a multi-regional trial can detect the variation among the regions more easily. [ABSTRACT FROM AUTHOR]

In this paper, the complete convergence for maximum of weighted sums of widely negative orthant dependent (WNOD) random variables are investigated. Some sufficient conditions for the convergence are provided and a relationship between the weight and the boundary function is revealed. Additionally, a Marcinkiewicz-Zygmund type strong law of large number for weighted sums of WNOD random variables is obtained. The results obtained in this paper generalize some corresponding ones for independent and some dependent random variables. As an application, the strong consistency for the weighted estimator in a non-parametric regression model is established. MR(2010) Subject Classification: 60F15; 62G05. [ABSTRACT FROM AUTHOR]

In this paper, we consider the kernel method to estimate sliced average variance estimation (SAVE). SAVE is a tool as SIR (sliced inverse regression), recommended to identify and to estimate the central dimension reduction (CDR) subspace. CDR subspace is the intersection of all dimension reduction subspaces which are at the base to describe the conditional distribution of the response Y given a d − dimensional predictor vector X. SAVE and even SIR are used to estimate CDR subspace. Two versions are very popular: slice version and kernel version. In this paper, we are looking at the kernel version. For Kernel SAVE version, two asymptotic properties have been demonstrated in particular: asymptotic normality and convergence in probability. And we know that these two properties, although important, are weak in front of almost sure convergence. However, until now, the strong consistency has not yet been obtained. In this paper, we obtain, under weaker assumptions, this asymptotic property. [ABSTRACT FROM AUTHOR]

The derivation of the sample covariance is difficult compared to that of the distribution of the sample correlation coefficient. This paper deals with the distributions of covariance structures appearing in real scalar/vector/matrix variables. Covariance structure is a bilinear structure. Consider a bilinear form u = X ′ A Y where X and Y are p × 1 and q × 1 real vectors and A is a constant p × q matrix. The basic aim in this paper is to derive the distribution of such a structure when the components are scalar/vector/matrix Gaussian variables. The procedure used is to examine the Laplace transform or the moment generating function (mgf) coming from such a bilinear form in real scalar/vector/matrix variables. Covariance structures in several situations are shown to produce a mgf of the type (1 − λ 2 t 2) − α , λ > 0 , α > 0 , − 1 λ < R (t) < 1 λ where t is the mgf parameter, R (·) means the real part of (·) , and λ and α are real scalar parameters. Explicit evaluation of the density of u is considered when α is a positive integer as well as for a general α. It is shown that the exact densities can be written as linear functions of double gamma densities and double exponential or Laplace densities when α is a positive integer. For the general value of α, it is shown that the exact density can be written in terms of double Mittag-Leffler or a double confluent hypergeometric function. [ABSTRACT FROM AUTHOR]