This paper is concerned with the problem of finding the minimax estimators of the scale parameter ? in a family of transformed chi-square distributions, under asymmetric squared log error (SLE) and modified linear exponential (MLINEX) loss functions, using the Lehmann Theorem [2]. Also we show that the results of Podder et al. [4] for Pareto distribution are a special case of our results for th...

We briefly introduce and discuss some criteria for optimal decisions. For the majority of this module, we consider a person’s utility for different options (or ‘rewards’ or ‘actions’) and, with uncertainty about the reward which will follow a specific decision, we aim at maximisation of the expected utility, which is actually the utility of the optimal decision (note that a decision is a gamble...

We propose a wavelet based regression function estimator for the estimation of the regression function for a sequence of ?-missing random variables with a common one-dimensional probability density function. Some asymptotic properties of the proposed estimator based on block thresholding are investigated. It is found that the estimators achieve optimal minimax convergence rates over large class...

In [12], new local minimax theorems which characterize a saddle point as a solution to a two-level local minimax problem are established. Based on the local characterization, a numerical minimax method is designed for finding multiple saddle points. Many numerical examples in semilinear elliptic PDE have been successfully carried out to solve for multiple solutions. One of the important issues ...

We investigate the problem of continuous-time causal estimation under a minimax criterion. Let X = {Xt, 0 ≤ t ≤ T} be governed by the probability law Pθ from a class of possible laws indexed by θ ∈ Λ, and Y T be the noise corrupted observations of X available to the estimator. We characterize the estimator minimizing the worst case regret, where regret is the difference between the causal estim...

let a be a banach algebra and e be a banach a-bimodule then s = a  e, the l1-direct sum of a and e becomes a module extension banach algebra when equipped with the algebras product (a; x):(a′; x′) = (aa′; a:x′ + x:a′). in this paper, we investigate △-amenability for these banach algebras and we show that for discrete inverse semigroup s with the set of idempotents es, the module extension bana...

let $r$ be a commutative ring with identity and $m$ be a finitely generated unital $r$-module. in this paper, first we give necessary and sufficient conditions that a finitely generated module to be a multiplication module. moreover, we investigate some conditions which imply that the module $m$ is the direct sum of some cyclic modules and free modules. then some properties of fitting ideals of...

a module $m$ is called $emph{h}$-cofinitely supplemented if for every cofinite submodule $e$ (i.e. $m/e$ is finitely generated) of $m$ there exists a direct summand $d$ of $m$ such that $m = e + x$ holds if and only if $m = d + x$, for every submodule $x$ of $m$. in this paper we study factors, direct summands and direct sums of $emph{h}$-cofinitely supplemented modules. let $m$ be an $emph{h}$...

in this paper, we establish some results on the existence of at least three weak solutions for adirichlet problem involving p-laplacian using a variational approach.

In this paper we defined the concept of module amenability of Banach algebras and module connes amenability of module dual Banach algebras.Also we assert the concept of module Arens regularity that is different with [1] and investigate the relation between module amenability of Banach algebras and connes module amenability of module second dual Banach algebras.In the following we studythe...