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.     

Estimating the order of moving average models: the max X2 method

The max X² technique for estimating rhe order of autoregressive processes (McClave (1976)) is extended to moving average models. The autöregressive-moving average duality is exploited by using the inverse autocorrelation function and the subset autoregression algorithm. The technique is demonstrated via simulations, and is applied to Box and Jenkins (1970) Series A.     

Univaiuate anu multivariate categorical data analysis for block designs

Analysis for univariate and multivariate categorical data in block designs is given and illustrated through examples. The univariate analysis compares the treatments on the basis of their pooled frequency distributions (pooled over blocks). The test statistic used is called Q after Cochran (1950). The large sample null distribution of Q is a chi-square. Analysis of p-variate categorical data (kth variable having ck classes, K=1,...,p) can be done by treating it as a univariate categorical problem with [d] classes. Very often [d] is large in relation to the size of the experiment. This makes the expected frequencies for some of the cells very small, making the univariate method inapplicable. In these circumstances it may be reasonable to compare the treatments on the basis of marginal distributions up to the mth dimension, 1[d] , which is given in this paper. This method is also illustrated for missing observations     

On variable selection in generalized linear and related regression models

This paper is concerned with selection of explanatory variables in generalized linear models (GLM). The class of GLM's is quite large and contains e.g. the ordinary linear regression, the binary logistic regression, the probit model and Poisson regression with linear or log-linear parameter structure. We show that, through an approximation of the log likelihood and a certain data transformation, the variable selection problem in a GLM can be converted into variable selection in an ordinary (unweighted) linear regression model. As a consequence no specific computer software for variable selection in GLM's is needed. Instead, some suitable variable selection program for linear regression can be used. We also present a simulation study which shows that the log likelihood approximation is very good in many practical situations. Finally, we mention briefly possible extensions to regression models outside the class of GLM's.     

On Calculations Involving the Maximum Cell Frequency

We describe a method of computing the cumulative distribution function of the maximum and minimum cell frequencies in sampling distributions commonly encountered in the analysis of categorical data.The procedure is efficient for exact or approximate calculation in both homogeneous and non-homogeneous cases, is non-recursive, and does not require Dirichlet integrals.Some related statistical problems are also discussed.     

Nonparametric Trend Estimation for Periodic Autoregressive Time Series

A periodically stationary time series has seasonal variances. A local linear trend estimation is proposed to accommodate unequal variances. A comparison of this proposed estimator with the estimator commonly used for a stationary time series is provided. The optimal bandwidth selection for this new trend estimator is discussed.     

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.