Abstract The problem of designing a robustified Kalman filtering technique, insensitive to spiky observations, or outliers, contaminating the Gaussian observations has been presented in paper. Firstly, class M-robustified dynamic stochastic approximation algorithms is derived by minimizing at each stage specific time-varying M-robust performance index, that is, general for family be considered....

Many results which are obtained or unable to by classical calculus have also been studied q-calculus. It is effective use q-calculus since it acts as a bridge between mathematics and physics. The q-analog of Chlodowsky operators has introduced the approximation properties these in [12]. Then [23], Stancu-Chlodowsky some via A-statistical convergence more general setting.In this paper, we presen...

This paper is devoted to studying the statistical approximation properties of a sequence univariate and bivariate blending-type Bernstein operators that includes shape parameters ? ? positive integer. An estimate corresponding rates was obtained, Voronovskaja-type theorem given by weighted A-statistical convergence. A Korovkin-type provided for cases operators. Moreover, convergence behavior ne...

In singular statistical models, it was shown that Bayes learning is effective. However, on Bayes learning, calculation containing the Bayes posterior distribution requires huge computational costs. To overcome the problem, mean field approximation (or equally variational Bayes method) was proposed. Recently, the generalization error and stochastic complexity in mean field approximation have bee...

The “large p, small n” paradigm arises in microarray studies, where expression levels of thousands of genes are monitored for a small number of subjects. There has been an increasing demand for study of asymptotics for the various statistical models and methodologies using genomic data. In this article, we focus on one-sample and two-sample microarray experiments, where the goal is to identify ...

We consider statistical models driven by Gaussian and non-Gaussian self-similar processes with long memory and we construct maximum likelihood estimators (MLE) for the drift parameter. Our approach is based in the non-Gaussian case on the approximation by random walks of the driving noise. We study the asymptotic behavior of the estimators and we give some numerical simulations to illustrate ou...

The aim of this paper is to give the set of all t-best approximations on fuzzy 2-normed linear spaces and prove some theorems in the sense of Vaezpour and Karimi [13]. AMS Subject Classification: 46A30, 46S40, 46A70, 54A40

Data cloning method is a new computational tool for computing maximum likelihood estimates in complex statistical models such as mixed models. The data cloning method is synthesized with integrated nested Laplace approximation to compute maximum likelihood estimates efficiently via a fast implementation in generalized linear mixed models. Asymptotic normality of the hybrid data cloning based di...