On the inadequacy of the customary orthogonal arrays in quality control and general scientific experimentation,and the need of probing designs of higher revealing power ∗

This paper breaks new ground concerning the general problem of factorial experimentation, namely, the identification and estimation of nonnegligible factorial effects (with minimal number of runs), without making the usual unrealistic and artificial assumptions concerning the negligibility of higher order interactions. (In other words, we consider the general factor screening problem when interactions may be present.) Through an example, it is shown that the customary orthogonal arrays fall short of the need. New principles for sieving the set of factorial effects to determine the large ones, are introduced. The concept of ‘revealing power’of designs, i.e. of their ability to help identify nonnegligible parameters is developed, and the usefulness in this direction of balanced arrays of full strength is studied.     

The coefficient of determination and its adjusted version in linear regression models

This article presents a comparative study of the efficiency properties of the coefficient of determination and its adjusted version in linear regression models when disturbances are not necessarily normal.     

Selection buasubg parameters in adaptive ridge regression estimators

Strawderman's family of regression estimators is considered. The choice of the scalars wbich characterize the biasing parameter is studied by obtaining the bias vector and the mean squared error matrix.     

Computation of standard errors in seemingly unrelated regression equation models

In a seemingly unrelated regression equation model, the feasible generalized least squares estimators are used for estimating the coefficients. In this paper, the standard errors associated with these estimators are obtained.     

Comparison of improved regression estimators with and without moments

For estimating the coefficients in a linear regression model, the double k–class estimators are considered and the small disturbance asymptotic approximation for their density function is obtained. Then employing the criterion of concentration probability around the true parameter values, a comparison is made between the estimators possessing finite moments and the estimators having no finite moments.     

Some characterizations of geometric tail distributions based on record values

Let R_j be the jth upper record value from an infinite sequence of independent identically distributed positive integer valued random variables. We show that their common distribution must have geometric tail if R_j+k?R_j and R_j are partially independent for some j≥1 and k≥1 or if E(R_j+2?R_j+1| R_j) is a constant. Three versions of partial independence, each of which provides a characterization of the geometric tail are presented.     

Properties of the ordinary least squares and stein-rule predictions in linear regression models with proxy variables

This article considers a linear regression model in which misspecification relates to the use of a stochastic proxy variable. The analysis indicates the decline in efficiency of the predictions arising from the ordinary least squares and the Stein-rule estimation procedures when a proxy variable is used in the place of an unobservable variable. However, the performance of the Stein-rule predictions is still found to be better than the ordinary least squares predictions over a broad range of k, the characterizing scalar of the Stein-rule estimator.     

Moments of the function of non-normal random vector with applications to econometric estimators and test statistics

In this paper we have provided a general result on the moments of a function of nonnormal random vector. The results for the normal case follow as a special case of this result. It is also indicated that the moments of a large class of econometric estimators and test statistics can be obtained by using our general result. This includes least squares estimator in the dynamic model, unit root tests, and the two step semiparametric estimators, among others.     

The asymptotic distribution of the likelihood ratio when the model is incorrect

Classical results on the asymptotic distribution of the likelihood ratio statistic rely on the assumption that the model chosen to construct the test statistic be correct. The model is said to be correct if it contains the true distribution of the observations. In this paper the asymptotic distribution of the likelihood ratio statistic is derived without the condition that the model need be correct.     

On-line control procedures under the random-walk model with measurement error and attribute observations

Assuming the quality characteristic process follows the random-walk model, the economic online control procedures are investigated by using the boundary correction technique when (1) the noise or measurement error follows either the random-walk model or the pure random model, and (2) the observations are taken by attributes only. Simple approximations for the long-run cost rate and optimal-control parameters are obtained.