Estimating the mean of the selected uniform population

Let π_i(i=1,2,…K) be independent U(0,?_i) populations. Let Y_i denote the largest observation based on a random sample of size n from the i-th population. for selecting the best populaton, that is the one associated with the largest ?_i, we consider the natural selection rule, according to which the population corresponding to the largest Y_i is selected. In this paper, the estimation of M. the mean of the selected population is considered. The natural estimator is positively biased. The UMVUE (uniformly minimum variance unbiased estimator) of M is derived using the (U,V)-method of Robbins (1987) and its asymptotic distribution is found. We obtain a minimax estimator of M for K≤4 and a class of admissible estimators among those of the form cY_max. For the case K = 2, the UMVUE is improved using the Brewster-Zidek (1974) Technique with respect to the squared error loss function L₁ and the scale-invariant loss function L₂. For the case K = 2, the MSE'S of all the estimators are compared for selected values of n and ρ=?₁/(?₁+?₂).     

Adjusting the bias of adaptive sampling estimators of spatial dispersion indexes by the δ-method

It is common practice to investigate the spatial dispersion in a community of discrete individuals (like animals or plants). Usually, the study area is partitioned into spatial units of equal size and then the relationship between the first two moments of the variable representing the number of individuals in each plot is investigated. When the points are spread over a very wide area so that the population density is low but many points are concentrated inside a few units, then a suitable sample method for estimating the first two moments is adaptive sampling. However, since the more common dispersion indexes are non linear function of the first two moments, the resulting estimators are biased for finite samples. Accordingly, a procedure to adjust bias is required for small samples. In this paper a δ-method evaluation of the bias is proposed and the asymptotic distribution of the bias-corrected estimators is provided. Finally, a simulation study is performed in order to investigate the performance of the proposed procedure.     

Standard errors in the multinomial logit model

Asymptotic stmdard errors in the multinomial log it model are derived for efficient estimates of (A) the probability of choosing an alternative , (B) the change in the probability of choosing an alternative given a change in an explanatory variable , (C) the expected response, and (D) the change in the expected response given a change in an explanatory variable. An empirical example illustrates the usefulness of the concepts developed here.     

Jackknife inference for heteroscedastic linear regression models

Inference on the regression parameters in a heteroscedastic linear regression model with replication is considered, using either the ordinary least-squares (OLS) or the weighted least-squares (WLS) estimator. A delete-group jackknife method is shown to produce consistent variance estimators irrespective of within-group correlations, unlike the delete-one jackknife variance estimators or those based on the customary δ-method assuming within-group independence. Finite-sample properties of the delete-group variance estimators and associated confidence intervals are also studied through simulation.