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.     

Inclusive Water Governance: a Global Necessity. Lessons from India

Efficient water management has emerged as a critical challenge of environmental protection and human security in the twenty-first century. Lack of water management affects the hydrological cycle of the earth, leading to a major influence on the livelihood of the people. This paper reviews the enhanced role of IWRM in water management. It discusses the functioning of Integrated Water Resource Management (IWRM) as a global approach to overcome the challenge(s) regarding the efficient management of water. Further, the paper argues for ‘inclusive water governance’ developed at the local level as against IWRM developed at the global level. The paper emphasizes on the approach of inclusive water governance as a practical solution to address the water management crisis in India, in particular, and developing countries, in general. Inclusive water governance is sensitive to equitable access to water, as a human right, and also to sustainability of water, as an important resource.

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.