Common fixed point theorem for hybrid generalized multi-valued contraction mappings

In this paper, we introduce the notion of a hybrid generalized multi-valued contraction mapping and establish the common fixed point theorem for this mapping. Our results generalize, unify, extend and complement several common fixed point theorems of many authors in the literature.     

Local Power Properties of Kernel Based Goodness of Fit Tests

If (X_i, i ) is a strictly stationary process with marginal density function f, we are interested in testing the hypothesis H₀: {f=f₀}, where f₀ is given. We consider different test statistics based on integrated quadratic forms measuring the proximity between f_n, a kernel estimator of f, and f₀, or between f_n and its expected value computed under H₀. We study the asymptotic local power properties of the testing procedures under local alternatives. This study generalizes to the multidimensional case in a context of dependence the corresponding one made by P. J. Bickel and M. Rosenblatt in 1973 (Ann. Statist.1, 1071–1095).     

检验的渐近展开和功效损失

本文研究统计假设检验问题中的渐近展开和功效损失,给出一阶渐近展开,二阶效率和功效损失,并且研究了建立在L－,R－,U－统计量及组合L－统计量上的检验问题。     

假设检验中p值的灵活运用

给出假设检验中p值的定义以及双边检验p值与单边检验p值的关系,介绍了利用p值将三种检验同时进行的方法及意义,最后给出应用实例.     

有关常数项级数的几个典型例题

通过实例考察常数项级数收敛和发散时一般项的一些特点,并讨论级数不满足比值判别法、根值判别法或莱布尼茨定理的条件时的收敛性问题.     

A transformed random effects model with applications

This paper proposes a transformed random effects model for analyzing non-normal panel data where both the response and (some of) the covariates are subject to transformations for inducing flexible functional form, normality, homoscedasticity, and simple model structure. We develop a maximum likelihood procedure for model estimation and inference, along with a computational device which makes the estimation procedure feasible in cases of large panels. We provide model specification tests that take into account the fact that parameter values for error components cannot be negative. We illustrate the model and methods with two applications: state production and wage distribution. The empirical results strongly favor the new model to the standard ones where either linear or log-linear functional form is employed. Monte Carlo simulation shows that maximum likelihood inference is quite robust against mild departure from normality. Copyright © 2009 John Wiley & Sons, Ltd.     

Absolute fixed point sets for multi-valued maps

The notion of a multi-valued absolute fixed point set (MAFS) will be defined and characterized in the setting of set-valued maps with images containing multiple components.

     

A Fixed Point Theorem for Multi—valued Composite Increasing Operators

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General auxiliary problem and algorithm for a generalized multi-valued variational-like inequality problem in reflexive Banach spaces

In this article, some generalized multi-valued variational-like inequality problems and their related general auxiliary problems in real reflexive Banach spaces are introduced. An existence theorem for one of the general auxiliary problems is proved. Furthermore, by exploiting this theorem, an algorithm for the corresponding generalized multi-valued variational-like inequality problem is constructed. The theorems of this article generalize, improve and unify many known corresponding results.     

Asymptotic distributions of non-central studentized statistics

Let X1,...,Xn be independent and identically distributed random variables and Wn = Wn(X1,...,Xn) be an estimator of parameter θ.Denote Tn =(Wn - θ0)/sn,where sn2 is a variance estimator of Wn.In this paper a general result on the limiting distributions of the non-central studen-tized statistic Tn is given.Especially,when s2n is the jacknife estimate of variance,it is shown that the limit could be normal,a weighted χ2 distribution,a stable distribution,or a mixture of normal and stable distribution.Applicati...