NONPARAMETRIC ESTIMATION OF THE GENERALIZED VARIANCE
For multivariate distributions with finite second order moments, a nonparametric symmetric, unbiased estimator of the generalized variance is considered, and it is shown to be (nonparametric) optimal for the class of distributions having finite fourth order moments. A jackknifed version of the sample generalized variance is also considered as a contender; it is computationally more convenient and asymptotically equivalent to the former. It is also shown that the second estimator performs quite well (in large sample) relative to the optimal normal theory estimators under several loss functions.

title: A Bayesian Approach to Optimum Allocation in Regression Problems

title: ESTIMATION IN THE MULTIPARAMETER EXPONENTIAL FAMILY: ADMISSIBILITY AND INADMISSIBILITY RESULTS
abstract: The problem of estimating k(äl) l inear combinations of the component means in the multiparameter exponential family with possibly dependent coordinates i s treated for squared-error loss. I t i s shown ρ that i f the natural parameter space is the whole of 1R , the UMVUE i s always admissible i f k s 2 . Also, suff ic ient conditions for admiss ibi l i ty of an arbitrary generalized Bayes estimate are obtained. I f the natural parameter space i s not the entire JR* (e.g. in the gamma case), inadmi s s ib i l i t y results are proved to indicate that the admiss ibi l i ty pattern of the "natural" estimate may be different even when k = l . F ina l ly , the problem of estimating a vector of smooth parametric functions more general than the means i s considered and admissible generalized Bayes estimates are obtained; in part icular, a result of Ghosh and Meeden (1977) follows as a corollary. AMS 1970 Subject C lass i f icat ions: Primary 62 C 15, Secondary 62 F 10

title: ESTIMATION OF A COMMON LOCATION OF SEVERAL EXPONENTIALS

title: INADMISSIBILITY OF THE BEST EQUIVARIANT ESTIMATORS OF THE VARIANCE-COVARIANCE MATRIX, THE PRECISION MATRIX, AND THE GENERALIZED VARIANCE UNDER ENTROPY LOSS
abstract: Based on a data matrix X = (X^ X^): pi k with independent columns Χ.;~Νη(ξ., Σ), and an independent ρχ ρ Wishart matrix S~W_(n,E), ι ρ ι -1 " estimators dominating the best equi variant estimators of Σ, Σ and |Σ| are obtained under two types of entropy loss. For simultaneous estimation of the mean vector and the variance-covariance matrix of a multinormal population, a suitable entropy loss is developed and estimators dominating the pair consisting of the sample mean vector and the best multiple of the sample Wishart matrix are derived. A technique of Sinha  is heavily exploited.

title: On the Equivalence of Confidence Sets Based on Bayesian and Non­Bayesian Procedures*:

title: RECURRENT FINSLER SPACE OF SECOND ORDER

title: ON RECURRENT SPACES OF SECOND ORDER IN FINSLER SPACES
abstract: By B. B. SINHA and S. P. SINGH ( Chaki and Roychowdhary have studied the Ricci recurrent spaces of second order in the Riemannian Geometry $[$ 1 $]$ . The object of present paper is to define the recurrent curvature tensor fields of second order and to study the properties of recurrence tensor field and the curvature tensor fields in the Finsler spaces.

title: Almost saturatedD-optimal main effect plans and allied results
abstract: The theory of unimodular matrices has been applied to deriveD-optimal main effect plans fors1 ×s2 factorials ins1 +s2 runs. Plans with highA-efficiency have also been given.