Asymptotic Results for Spatial ARMA Models

Causal quadrantal-type spatial ARMA(p, q) models with independent and identically distributed innovations are considered. In order to select the orders (p, q) of these models and estimate their autoregressive parameters, estimators of the autoregressive coefficients, derived from the extended Yule–Walker equations are defined. Consistency and asymptotic normality are obtained for these estimators. Then, spatial ARMA model identification is considered and simulation study is given.     

An extension of bayesian measure of information to regression

This paper extends Lindley's measure of average information to the linear model, E(Y∣ß) = Xß. An expression which quantifies the average amount of information provided by the nxl vector of observations Y about the pxl vector of coefficient parameters ß will be derived. The effect of the structure of the regressor matrix, X, on the information measure is discussed. An information theoretic optimal design is characterized. Some applications are suggested.     

An asymptotic distribution-free selection procedure for a two-way layout problem

This paper deals with an asymptotic distribution-free subset selection procedure for a two-way layout problem. The treatment effect with the largest unknown value is of interest to us. The block effect is a nuisance parameter in this problem. The proposed procedure is based on the Hodges-Lehmann estimators of location parameters. The asymptotic relative efficiency of the proposed procedure with the normal means procedure is evaluated. It is shown that the proposed procedure has a high efficiency.     

Bootstrap method in ranking and slippage problems

In this paper, the bootstrap method of Efron (1979) is given for a ranking and a slippage problem, where the ranking (or slippage) is with respect to the mean of the distributions. The method is also applied to obtain a confidence interval for the largest mean.     

Least significant spacing for ‘one versus the rest’ normal populations

Consider sample means from k(≥2) normal populations where the variances and sample sizes are equal. The problem is to find the ‘least significant difference’ or ‘spacing’ (LSS) between the two largest means, so that if an observed spacing is larger we have confidence 1 - α that the population with largest sample mean also has the largest population mean.

When the variance is known it is shown that the maximum LSS occurs when k = 2, provided a < .2723. In other words, for any value of k we may use the usual (one-tailed) least significant difference to demonstrate that one population has a population mean greater than (or equal to) the rest.

When the variance is estimated bounds are obtained for the confidence which indicate that this last result is approximately correct.     

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).     

Unbiased estimation of the parameter of a selected binomial population

The problem is to estimate the parameter of a selected binomial population. The selction rule is to choose the population with the greatest number of successes and, in the case of a tie, to follow one of two schemes: either choose the population with the smallest index or randomize among the tied populations. Since no unbiased estimator exists in the above case, we employ a second stage of sampling and take additional observations on the selected population. We find the uniformly minimum variance unbiased estimator (UMVUE) under the first tie break scheme and we prove that no UMVUE exists under the second. We find an unbiased estimator with desirable properties in the case where no UMVUE exists.     

An alternative approach to variable selection for prediction

A procedure for selecting a subset of predictor variables in regression analysis is suggested. The procedure is so designed that it leads to the selection of a subset of variables having an adequate degree of informativeness with a directly specified confidence coefficient. Some examples are considered to illustrate the application of the procedure.     

A plug-in technique in nonparametric regression with dependence

The problem addressed is that of smoothing parameter selection in kernel nonparametric regression in the fixed design regression model with dependent noise. An asymptotic expression of the optimum bandwidth parameter has been obtained in recent studies, where this takes the form h = C ₀ n ^?1/5. This paper proposes to use a plug-in methodology, in order to obtain an optimum estimation of the bandwidth parameter, through preliminary estimation of the unknown value of C ₀.