The death of Professor K. C. Sreedharan Pillai on June 5, 1985 was a heavy loss to many statisticians all around the world. This volume is dedicated to his memory in recog­ nition of his many contributions in multivariate statis­ tical analysis. It brings together eminent statisticians Working in multivariate analysis from around the world. The research and expository papers cover a cross-section of recent developments in the field. This volume is especially useful to researchers and to those who want to keep abreast of the latest directions in multivariate statistical analysis. I am grateful to the authors from so many different countries and research institutions who contributed to this volume. I wish to express my appreciation to all those who have reviewed the papers. The list of people include Professors T. C. Chang, So-Hsiang Chou, Dipak K. Dey, Peter Hall, Yu-Sheng Hsu, J. D. Knoke, W. J. Krzanowski, Edsel Pena, Bimal K. Sinha, Dennis L. Young, Drs. K. Krishnamoorthy, D. K. Nagar, and Messrs. Alphonse Amey, Chi-Chin Chao and Samuel Ofori-Nyarko. I wish to thank Professors Shanti S. Gupta and James 0. Berger for their keen interest and encouragement. Thanks are also due to Cynthia Patterson for her help and Reidel Publishing Com~any for their cooperation in bringing this volume out.

Minimaxity of Empirical Bayes Estimators Derived from Subjective Hyperpriors.- Quasi-Inner Products and Their Applications.- A Hierarchy of Relationships Between Covariance Matrices.- Effect of Additional Variables in Principal Component Analysis, Discriminant Analysis and Canonical Correlation Analysis.- On a Locally Best Invariant and Locally Minimax Test in Symmetrical Multivariate Distributions.- Confidence Intervals for the Slope in a Linear Errors-in-Variables Regression Model.- Likelihood Ratio Test for Multisample Sphericity.- Statistical Selection Procedures in Multivariate Models.- Quadratic Forms to have a Specified Distribution.- Asymptotic Expansions for Errors of Misclassification:Nonnormal Situations.- Transformations of Statistics in Multivariate Analysis.- Error Rate Estimation in Discriminant Analysis: Recent Advances.- Some Simple Optimal Tests in Multivariate Analysis.- Developments in Eigenvalue Estimation.- Asymptotic Non-null Distributions of a Statistic for Testing the Equality of Hermitian Covariance Matrices in the Complex Gaussian Case.- A Model for Interlaboratory Differences.- Bayes Estimators in Lognormal Regression Model.- Multivariate Behrens-Fisher Problem by Heteroscedastic Method.- Tests for Covariance Structure in Familial Data and Principal Component.- Risk of Improved Estimators for Generalized Variance and Precision.- Sampling Distributions of Dependent Quadratic Forms from Normal and Nonnormal Universes.- Bibliography of Works by K. C. S. Pillai.