Estimation in Singular Linear Models with Stochastic Linear Restrictions and Linear Equality Restrictions

This article is concerned with the parameter estimation in a singular linear regression model with stochastic linear restrictions and linear equality restrictions simultaneously. A new estimator is introduced and it is proved that the proposed estimator is superior to the least squares estimator and singular mixed estimator in the mean squared error sense under certain conditions.     

Local Linear Estimation of Recurrent Jump—Diffusion Models

In this article, we provide a nonparametric estimation of first and second infinitesimal moments of the underlying jump diffusion model. We show that under certain regularity conditions the nonparametric estimations of first and second infinitesimal moments based on the local linear estimator are consistent and asymptotically follow normal distributions.     

Multivariate Aging with Archimedean Dependence Structures in High Dimensions

Bivariate aging notions for a vector X of lifetimes based on stochastic comparisons between X and X _t, where X _t is the multivariate residual lifetime after time t > 0, have been studied in Pellerey (2008 Pellerey , F. ( 2008 ). On univariate and bivariate aging for dependent lifetimes with Archimedean survival copulas . Kybernetika 44 : 795 – 806 .[Web of Science ®] , [Google Scholar]) under the assumption that the dependence structure in X is described by an Archimedean survival copula. Similar stochastic comparisons between X _t and X _t+s, for all t; s > 0, were considered in Mulero and Pellerey (2010 Mulero , J. , Pellerey , F. ( 2010 ). Bivariate aging properties under Archimedean dependence structures . Commun. Statist. Theor. Meth. 39 : 3108 – 3121 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]). In this article, these results are generalized and extended to the multivariate case. Two illustrative examples are also provided.     

The Homogeneous Markov System (HMS) as an Elastic Medium. The Three-Dimensional Case

Every attainable structure of the so-called continuous-time Homogeneous Markov System (HMS) with fixed size and state space S = {1, 2,…, n} is considered as a particle of R ⁿ and, consequently, the motion of the structure corresponds to the motion of the particle. Under the assumption that “the motion of every particle-structure at every time point is due to its interaction with its surroundings,” R ⁿ becomes a continuum (Tsaklidis, 1998 Tsaklidis , G. ( 1998 ). The continuous time homogeneous Markov system with fixed size as a Newtonian fluid? Appl. Stoch. Mod. Data Anal. 13 : 177 – 182 .[Crossref] , [Google Scholar]). Then the evolution of the set of the attainable structures corresponds to the motion of the continuum. For the case of a three-state HMS it is stated that the concept of the two-dimensional isotropic elasticity can further be used to interpret the three-state HMS's evolution.     

SCAD-Penalized Least Absolute Deviation Regression in High-Dimensional Models

When outliers and/or heavy-tailed errors exist in linear models, the least absolute deviation (LAD) regression is a robust alternative to the ordinary least squares regression. Existing variable-selection methods in linear models based on LAD regression either only consider the finite number of predictors or lack the oracle property associated with the estimator. In this article, we focus on the variable selection via LAD regression with a diverging number of parameters. The rate of convergence of the LAD estimator with the smoothly clipped absolute deviation (SCAD) penalty function is established. Furthermore, we demonstrate that, under certain regularity conditions, the penalized estimator with a properly selected tuning parameter enjoys the oracle property. In addition, the rank correlation screening method originally proposed by Li et al. (2011 Li, G.R., Peng, H., Zhu, L.X. (2011). Nonconcave penalized M-estimation with a diverging number of parameters. Statistica Sinica 21:391–419.[Web of Science ®] , [Google Scholar]) is applied to deal with ultrahigh dimensional data. Simulation studies are conducted for revealing the finite sample performance of the estimator. We further illustrate the proposed methodology by a real example.     

Further results on discrete mean past lifetime

Abstract

The present paper aims at studying the mean past lifetime of a discrete random variable. The notion of discrete mean past lifetime is studied in relation to the concepts of reversed hazard rate, reversed lack of memory property, and cumulative past entropy. New classes of distributions characterized by particular forms of discrete mean past life are also investigated. Implications of an increasing mean past lifetime on other reliability notions are studied and finally some bivariate generalizations are discussed.     

Stochastic comparisons of two-unit repairable systems

Abstract

We consider two models of two-unit repairable systems: cold standby system and warm standby system. We suppose that the lifetimes and repair times of the units are all independent exponentially distributed random variables. Using stochastic orders we compare the lifetimes of systems under different assumptions on the parameters of exponential distributions. We also consider a cold standby system where the lifetimes and repair times of its units are not necessarily exponentially distributed.     

Simultaneous estimation of gamma means using a hierarchical generalized linear model

The problem of simultaneously estimating p Gamma means is investigated when the means are believed a priori to satisfy an r-dimensional generalized linear model. Using a Bayesian hierarchical model to reflect the uncertainty in the linear model, approximate methods are proposed to compute the posterior densities. The resulting estimator shrinks the usual estimator toward a prior estimator where the size of the shrinkage depends upon the agreement of the observed data with the proposed generalized linear model.     

Some stochastic orders of dynamic additive mean residual life model

Sometimes additive hazard rate model becomes more important to study than the celebrated (Cox, 1972) proportional hazard rate model. But the concept of the hazard function is sometimes abstract, in comparison to the concept of mean residual life function. In this paper, we have defined a new model called ‘dynamic additive mean residual life model’ where the covariates are time dependent, and study the closure of this model under different stochastic orders.     

Bayesian Analysis of Stochastic Volatility Models

New techniques for the analysis of stochastic volatility models in which the logarithm of conditional variance follows an autoregressive model are developed. A cyclic Metropolis algorithm is used to construct a Markov-chain simulation tool. Simulations from this Markov chain converge in distribution to draws from the posterior distribution enabling exact finite-sample inference. The exact solution to the filtering/smoothing problem of inferring about the unobserved variance states is a by-product of our Markov-chain method. In addition, multistep-ahead predictive densities can be constructed that reflect both inherent model variability and parameter uncertainty. We illustrate our method by analyzing both daily and weekly data on stock returns and exchange rates. Sampling experiments are conducted to compare the performance of Bayes estimators to method of moments and quasi-maximum likelihood estimators proposed in the literature. In both parameter estimation and filtering, the Bayes estimators outperform these other approaches.