On the choice of transformations of the correlation coefficient with or without an outlier

Five transformations of the correlation coefficient, namely, Fisher's z, Nair's u, Sankaran's v, Ruben's y and Samiuddin's t are compared numerically using confidence intervals. Samiuddin's t_s transformation is close to the exact nominal confidence level for a small sample size ≤ 25 from a bivariate normal density. For a sample size > 25 both Samiuddin's t_s and Fisher's z can be used. In the presence of an outlier (on a minor axis), both Fisher's z and Samiuddin's t_s are not affected as long as |p| ≤ 0.3 but are seriously affected when |p&| > 0.3.     

On the distribution of hotelling's t2 and multiple correlation r2when sampling from a mixture of two normals

In this paper the non-null distribution of Hotelling's T² and the null distribution of multiple correlation R² are derived when the sample is taken from a mixture of two p-component multivariate normal distributions with mean vectors μ₁ and μ₂ respectively and common covariance matrix ∑, ∑. In a special case the non-null distribution of R² is a l s o given, while the general noncentral distribution is given i n Awan (1981). These results have been used to study the robustness of T² and R² tests by Srivastava and Awan (1982), and Awan and Srivastava (1982) respectively.     

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.     

Main effect plan for 2m factorials which allow search and estimation of one unknown effect

In this paper, we discuss resolution III plans for 2^m factorial experiments which have an additional property. We relax the classical assumption that all the interactions are negligible by assuming that (at most) one of them may be nonnegligible. Which interaction is nonnegligible is unknown. We discuss designs which allow the search and estimation of this interaction, along with the estimation of the general mean and the main effects as in the classical resolution III designs.     

Bias and mean squared error of the slope estimator in a regression with not necessarily normal errors in both variables

The least squares estimation of the slope parameter of a simple linear regression is biased if the regressor variable is measured with random errors. This bias as well as the mean squared error is computed up to the order of 1/T without assuming normality for the error variable. They depend on the fourth moment of the error variable.