Double Sampling Ratio-product Estimator of a Finite Population Mean in Sample Surveys

It is well known that two-phase (or double) sampling is of significant use in practice when the population parameter(s) (say, population mean X¯) of the auxiliary variate x is not known. Keeping this in view, we have suggested a class of ratio-product estimators in two-phase sampling with its properties. The asymptotically optimum estimators (AOEs) in the class are identified in two different cases with their variances. Conditions for the proposed estimator to be more efficient than the two-phase sampling ratio, product and mean per unit estimator are investigated. Comparison with single phase sampling is also discussed. An empirical study is carried out to demonstrate the efficiency of the suggested estimator over conventional estimators.     

Comparison of estimators of the location parameter using pitman's closeness criterion

Necessary and sufficient conditions for a linear estimator to dominate another linear estimator of a location parameter under the Pitman's criterion of comparison are discussed. Consequently it is demonstrated that a linear biased estimator can not dominate a linear unbiased estimator under Pitman's criterion and that the sample mean is the Closest Linear Unbiased Estimator (CLUE). It is also shown that the ridge regression estimator with a known biasing constant can not dominate the ordinary least squares estimator. If an estimator δdominates an estimator δin the average loss sense then sufficient conditions are obtained under which δis also preferred over δunder Pitman's criterion. Further we obtain sufficient conditions under which preference under the Pitman's criterion will lead to preference under the mean squared error sense.     

On the relative accuracy of certain bootstrap procedures

We show the second-order relative accuracy, on bounded sets, of the Studentized bootstrap, exponentially tilted bootstrap and nonparametric likelihood tilted bootstrap, for means and smooth functions of means. We also consider the relative errors for larger deviations. Our method exploits certain connections between Edgeworth and saddlepoint approximations to simplify the computations.     

A Measure of partial association between disease and genotype for the two-parent problem

The two-parent disease-genotype association problem is studied from the point of view of a coefficient of association between the disease phenotype of the child and the disease phenotypes of the parents, in the presence of some genotypic information about the parents. This coefficient of partial association is derived, and certain tests of hypotheses are constructed. The results are shown to be useful in estimation of recurrence risks, and in understanding the nature of the association between child and parental disease phenotypes.     

On Robust Analysis of a Normal Location Parameter

Pericchi and Smith considered a normal location parameter problem with double-exponential and Student t prior distributions. These two prior distributions both belong to the class of scale mixtures of normal distributions and are useful in providing a robust analysis of the normal location parameter problem. In this paper we extend the analysis to other scale mixtures of normal distributions, such as the exponential power and the symmetric stable distributions.     

SOME SECOND ORDER ASYMPTOTICS IN EXPONENTIAL FAMILY NON-LINEAR REGRESSION MODELS (A GEOMETRIC APPROACH)

The differential geometric framework of Amari (1982a, 1985) is applied to the study of some second order asymptotics related to the curvatures for exponential family nonlinear regression models, in which the observations are independent but not necessarily identically distributed. This paper presents a set of reasonable regularity conditions which are needed to study asymptotics from a geometric point of view in regression models. A new stochastic expansion of a first order efficient estimator is derived and used to study several asymptotic problems related to Fisher information in terms of curvatures. The bias and the covariance of the first order efficient estimator are also calculated according to the expansion.     

A Construction of Lancaster Probabilities with Margins in the Multidimensional Meixner Class

The well-known Meixner class (Meixner, 1934) of probabilities on R has been extended recently to R ^d (Pommeret, 1996). This generalized Meixner class corresponds to the simple quadratic natural exponential families characterized by Casalis (1996). Following Lancaster (1975), the present paper offers a characterization of the joint probability of a randomvector ( X, Y ) such that the two variables X and Y on R ^d belong to the multidimensional Meixner class and fulfil a bi-orthogonality condition involving orthogonal polynomials. The joint probabilities, called Lancaster probabilities, are characterized by two sequences of orthogonal polynomials with respect to the margins and a sequence of expectations of products. Some multivariate probabilities are studied, namely the Poisson-Gaussian and the gamma-Gaussian.     

具单一休假的M/M/1排队模型的指数稳定性

研究具单一休假的M/M/1排队模型,使用泛函分析方法,特别是Banach空间上线性算子理论,证明了相应的动力算子的严格占优本征值的存在性,以及系统解的线性稳定性和指数稳定性.     

Robustness of Parameter Estimation Procedures in Multilevel Models When Random Effects are MEP Distributed

In this paper we examine maximum likelihood estimation procedures in multilevel models for two level nesting structures. Usually, for fixed effects and variance components estimation, level-one error terms and random effects are assumed to be normally distributed. Nevertheless, in some circumstances this assumption might not be realistic, especially as concerns random effects. Thus we assume for random effects the family of multivariate exponential power distributions (MEP); subsequently, by means of Monte Carlo simulation procedures, we study robustness of maximum likelihood estimators under normal assumption when, actually, random effects are MEP distributed.     

Estimating the Upper Support Point in Deconvolution

Abstract.  We consider estimation of the upper boundary point F ⁻¹ (1) of a distribution function F with finite upper boundary or 'frontier' in deconvolution problems, primarily focusing on deconvolution models where the noise density is decreasing on the positive halfline. Our estimates are based on the (non-parametric) maximum likelihood estimator (MLE) of F . We show that (1) is asymptotically never too small. If the convolution kernel has bounded support the estimator (1) can generally be expected to be consistent. In this case, we establish a relation between the extreme value index of F and the rate of convergence of (1) to the upper support point for the 'boxcar' deconvolution model. If the convolution density has unbounded support, (1) can be expected to overestimate the upper support point. We define consistent estimators , for appropriately chosen vanishing sequences ( β _n ) and study these in a particular case.