Sequential unbiased estimation of parameters in a two-way contingency table

Classical analysis of contingency tables employs (i) fixed sample sizes and (ii) the maximum likelihood and weighted least squares approach to parameter estimation. It is well-known, however, that certain important parameters, such as the main effect and interaction parameters, can neverbe estimated unbiasedly when the sample size is fixed a priori We introduce a sequential unbiased estimator for the cell probabilities subject to log linear constraints. As a simple consequence, we show how parameters such as those mentioned above may. be estimated unbiasedly. Our unbiased estimator for the vector of cell probabilities is shown to be consistent in the sense of Wolfowitz (Ann. Math. Statist. (1947) 18). We give a sufficient condition on a multinomial stopping rule for the corresponding sufficient statistic to be complete. When this condition holds, we have a unique minimum variance unbiased estimator for the cell probabilities.     

Comparing the BLUEs Under Two Linear Models

In this article, we consider two linear models, ?₁ = {y, X β, V ₁} and ?₂ = {y, X β, V ₂}, which differ only in their covariance matrices. Our main focus lies on the difference of the best linear unbiased estimators, BLUEs, of X β under these models. The corresponding problems between the models {y, X β, I _n } and {y, X β, V}, i.e., between the OLSE (ordinary least squares estimator) and BLUE, are pretty well studied. Our purpose is to review the corresponding considerations between the BLUEs of X β under ?₁ and ?₂. This article is an expository one presenting also new results.     

On partial sufficiency: A review

The notion of a sufficient statistic—a statistic that summarizes in itself all the relevant information in the sample x about the universal parameter ω—is acclaimed as one of the most significant discoveries of Sir Ronald A. Fisher. It is however not well-recognized that the related notion of a partially sufficient statistic—a statistic that isolates and exhausts all the relevant and usable information in the sample about a sub-parameter θ=θ(ω)—can be very elusive if the question is posed in sample space terms. In this review article, the author tries to unravel the mystery that surrounds the notion of partial sufficiency. For mathematical details on some of the issues raised here one may refer to Basu (1977).     

Umbrella for research into Human Resource Development (HRD)

This paper explores Thailand's ‘sufficiency economy’ (SE) philosophy and its impact on human resource development (HRD). The paper highlights the current attempts to achieve sustainable development, especially after the economic crisis of 1997. The philosophy introduces a great shift of conceptual thinking on the general development and administration in the country. This paper examines the importance of the SE philosophy and discusses its impact on HRD in Thailand at different levels of the society.     

Ignorability, Sufficiency and Ancillarity

This paper explores the relationship between ignorability, sufficiency and ancillarity in the coarse data model of Heitjan and Rubin. Bayes or likelihood ignorability has a natural relationship to sufficiency, and frequentist ignorability an analogous relationship to ancillarity. Weaker conditions, termed observed likelihood sufficiency, observed specific sufficiency and observed ancillarity, expand the concepts to models where the coarsening mechanism is sometimes, but not always, ignorable.     

Exchangeability,predictive sufficiency and Bayesian bootstrap

Summary Let {X _n } be a sequence of random variables conditionally independent and identically distributed given the random variable Θ. The aim of this paper is to show that in many interesting situations the conditional distribution of Θ, given (X ₁,…,X _n ), can be approximated by means of the bootstrap procedure proposed by Efron and applied to a statisticT _n (X ₁,…,X _n ) sufficient for predictive purposes. It will also be shown that, from the predictive point of view, this is consistent with the results obtained following a common Bayesian approach.     

Information,ancillarity, and sufficiency in the presence of nuisance parameters

The Fisher information about parameters of interest (P-information) is invariant with respect to nuisance parameters, and induces an information inequality associated with likelihood factorization. This information inequality provides a natural basis for measuring information loss due to using only a sublikelihood function for inference. In contrast with the global reparametrization of some previous concepts in the literature, the concepts of P-ancillarity and P-sufficiency proposed in this article are characterized by the notion of no pointwise information loss with respect to the parameters of interest. A conditional version of P-sufficiency is also proposed. The asymptotic efficiency of likelihood inference under P-ancillarity or P-sufficiency is outlined.     

Optimal Estimator for Logistic Model with Distribution‐free Random Intercept

Logistic models with a random intercept are prevalent in medical and social research where clustered and longitudinal data are often collected. Traditionally, the random intercept in these models is assumed to follow some parametric distribution such as the normal distribution. However, such an assumption inevitably raises concerns about model misspecification and misleading inference conclusions, especially when there is dependence between the random intercept and model covariates. To protect against such issues, we use a semiparametric approach to develop a computationally simple and consistent estimator where the random intercept is distribution‐free. The estimator is revealed to be optimal and achieve the efficiency bound without the need to postulate or estimate any latent variable distributions. We further characterize other general mixed models where such an optimal estimator exists.     

证据充分性的逻辑分析

从逻辑思考方法的角度,在思维形式与思维规律的层面上对如何运用证据,特别是运用间接证据认定案件主要事实(主要是在刑事案件中)如何判定证据充分性的问题进行探讨。     

Panel Binary Variables and Sufficiency: Generalizing Conditional Logit

This paper extends the conditional logit approach (Rasch, Andersen, Chamberlain) used in panel data models of binary variables with correlated fixed effects and strictly exogenous regressors. In a two‐period two‐state model, necessary and sufficient conditions on the joint distribution function of the individual‐and‐period specific shocks are given such that the sum of individual binary variables across time is a sufficient statistic for the individual effect. By extending a result of Chamberlain, it is shown that root‐n consistent regular estimators can be constructed in panel binary models if and only if the property of sufficiency holds. In applied work, the estimation method amounts to quasi‐differencing the binary variables as if they were continuous variables and transforming a panel data model into a cross‐section model. Semiparametric approaches can then be readily applied.