Adaptive sequential confidence intervals for A location Parameter

Let θ + X₁, θ + X₂... be a random sample and X_i's have a common distribution function F, where F has an absolutely continuous density f that is symmetric about origin. For a given confidence coefficient, a fully sequential procedure is proposed for constructing a fixed-width confidence interval for the location parameter θ. The result is based on Stone's (1975) adaptive maximum likelihood estimator. under mild conditions the procedure is shown to be asymptotically consistent and fully efficient.     

Replicated piecewise stopping numbers and sequential analysis

For certain basic problems in sequential analysis,it is shown that a piecewise sequential methodology resting on replicated piecewise stopping numbers provides a natural estimate of the variance of the overall stopping variable without compromising much on the performancecharacteristics of the estimation rules.     

Fixed-width confidence interval of log odds ratio for joint binomial and inverse binomial sampling

This article provides a two-stage procedure to develop a fixed-width confidence interval of log odds ratio in a joint binomial and inverse binomial setting where the stopping rule is obtained by adopting a two-stage procedure on the number of index subjects for the inverse sampling. A purely sequential version of this procedure is also studied. Different asymptotic results associated with the procedures are obtained. The findings are supported by detailed simulation study followed by one data example.     

On Two-Stage Sampling for Fixed-Width Interval Estimation of the Common Variance of Equi-Correlated Normal Distributions

Abstract

The present article presents two-stage procedures for fixed-width interval estimators of the common variance of equi-correlated normal distributions. This study is a continuation of those of Zacks and Ramig (1987 Zacks , S. and Ramig , P. ( 1987 ). Confidence Intervals for the Common Variance of Equicorrelated Normal Random Variables , in Contributions to the Theory and Applications of Statistics, A Volume in Honor of Herbert Soloman , New York : Academic Press . [Google Scholar]) and Ghezzi and Zacks (2005 Ghezzi , D. J. and Zacks , S. ( 2005 ). Inference on the Common Variance of Correlated Normal Random Variables , Communications in Statistics - Theory and Methods 34 : 1517 – 1531 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]). We derive formulae for the distributions of total sample sizes and their functionals.     

Fixed width interval estimation for the multiple response callibration problem

A multiple response extension is proposed for the univariate calibration problem and a sequential solution is developed. The sequential sampling procedure is a generalization of existing univariate results of Perng and Tong (1974) and is based on the theory developed by Chow and Robbins (1965). It is shown that the proposed multiple response procedure is at least as good as and in many instances better than the univariate method     

On asymptotically Risk-effivient sequential versions of generalized U-statistics

Sequential point estimation of means of generalized U-statistics is considered. Based on a well defined stopping rule, the proposed sequential (estimation) procedure is shown to be asymptotically (first order) risk-efficient. Asymptotic distributions of sequential generalized U-statistics and the allied stopping times are also studied.     

A note on the CFR inequality for sequential estimation

Considering the regu1ar j.i.d. case, this note points out that Govindarajalu and Vincze(1989) are mistaken in claiming that their lower bound for the variance of sequential estimators is better than that of Wolfowitz (1847) by showing that the two bounds are identical.     

A three-stage procedure based on bootstrap critical points

The construction of fixed-width confidence intervals for an unknown population parameter is often based on the normal approximation of an appropriate statistic. In this paper we follow a different approach using bootstrap appro¬ximations, which are known to have a high degree of accuracy. It is expected that such an approximation leads to better results, at least in the second order behaviour.In order to avoid computationally very costly procedures,inherent to a fully sequential method,we implement the bootstrap ideas in a three-stage procedure.Simulation results illustrate the performance of the proposed procedure for small and moderate sample sizes.To support the method we establish some basic asymptotic properties.     

MULTIVARIATE LOCAL POLYNOMIAL REGRESSION FOR TIME SERIES:UNIFORM STRONG CONSISTENCY AND RATES

Abstract. Local high-order polynomial fitting is employed for the estimation of the multivariate regression function m ( x₁ ,… x_d ) = E {φ( Y_d )φ X ₁= x ₁,…, X_d = x_d }, and of its partial derivatives, for stationary random processes { Y_i , X_i }. The function φ may be selected to yield estimates of the conditional mean, conditional moments and conditional distributions. Uniform strong consistency over compact subsets of R_d , along with rates, are established for the regression function and its partial derivatives for strongly mixing processes.     

sequential estimation of the hgarginal density function for a strongly mixing process

Suppose that {X_n} is a strongly mixing process with unknow marginal density f(x) and that we estimate f(x) by a kernel estimator [fcirc]_n(x|h_n)and want to achive the MISE no larger than some preassigned postive number w. However,the appropriate sample size n^*depends on a functional of the unknow density function. Therefore some sequential procedure is required and we adopt a fully sequential procedure. In this paper we investigate the asymptotic properties of the procedure and show that the producure is asymptotically efficient in a certain sense as w→0. The results are almost the same in the i.i.d. setting. our result extend a class of models to which the methodology can be applied. For example economic variable,experiments on a single subject in which obervation are not indepent, and so on.     

Sequential methodologies for comparing exponential mean survival times

Sequential methodologies are derived for comparing arbitrary number of exponential mean survival times when the loss function is squared error plus the cost of sampling. From the theoretical point of view, we have given derivations of the asymptotic second-order expansi6n of the. risk function and bias associated with the proposed sequential estimator. We have noted, via computer simulations, that these expansions lead to useful guidelines even for small as well as moderate sample sizes.     

Robust estimators under semi‐parametric partly linear autoregression: Asymptotic behaviour and bandwidth selection

Abstract. In this article, under a semi‐parametric partly linear autoregression model, a family of robust estimators for the autoregression parameter and the autoregression function is studied. The proposed estimators are based on a three‐step procedure, in which robust regression estimators and robust smoothing techniques are combined. Asymptotic results on the autoregression estimators are derived. Besides combining robust procedures with M‐smoothers, predicted values for the series and detection residuals, which allow to detect anomalous data, are introduced. Robust cross‐validation methods to select the smoothing parameter are presented as an alternative to the classical ones, which are sensitive to outlying observations. A Monte Carlo study is conducted to compare the performance of the proposed criteria. Finally, the asymptotic distribution of the autoregression parameter estimator is stated uniformly over the smoothing parameter.     

基于规则的国际炼化工程施工费用快速估算

建立了国际炼化工程项目分专业的费用工作综合指标体系和相应的施工费用快速估算规则,明确了规则的应用条件,并结合应用实例说明了分级指标的应用,验证了所提出的快速估算方法的有效性.提出方法对国际炼化工程项目施工费的快速估算和投标报价分析评估具有较好的实用价值.     

Sequential and two-stage point estimation for the range in a power family distribution

Sequential and two-stage point estimation procedures for the range of a power family distribution are discussed using a loss function from a fairly general class.

Some asymptotic characteristics of the sequential procedure are presented, including approximate expressions for the distribution of the sample size. For the two stage procedure, we present asymptotic properties and exact expressions for the risk of the procedure, and distribution and mean of the stopping rule. The results of numerical simulations are presented to demonstrate some practical merits of our procedures for moderate sample sizes.     

Sequential procedures for monltoring the parameters of the autoregressive model relative to unspecified targets

Sequential procedures are developed for monitoring the parameters of a time dependent autoregressive model relative to unspecified targets. Such a problem arises when we need to monitor the parameters for changes from their unknown initial values (the unspecified targets), instead of from specified targets. For this purpose, scores type statistics are proposed which: (1) reflect changes in the parameters from their initial values without requiring any input about these values; and (2) are aimed at detecting arbitrary shifts in the parameters, instead of at restrictive "one point" shift alternatives. The procedures developed are capable of monitoring any one of, or any combination of, the mean, variance or correlation structure of an autoregressive sequence of known finite order. Their false signal rates are controlled, and their performance under local shift     

集成材料粘合工艺因素解析

本文根据我国目前家具行业的生产需求,对集成材胶粘剂使用工艺过程进行工序分解,并对各工序的关键工艺因素予以解析,以便合理地粘接工艺,确保家具的质量。