117630231
ON THE RECURRENT TENSOR FIELDS OF FINSLER SPACES
118248820
RECURRENT FINSLER SPACE OF SECOND ORDER
115388755
ON RECURRENT SPACES OF SECOND ORDER IN FINSLER SPACES
By B. B. SINHA and S. P. SINGH (Received Feb. 20, 1970) Summary. 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.
121240340
NONPARAMETRIC ESTIMATION OF THE GENERALIZED VARIANCE
Abstract : 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. (Keywords: kernels; U-statistics; von mises' functionals).
125185293
A Bayesian Approach to Optimum Allocation in Regression Problems
122032644
Almost saturatedD-optimal main effect plans and allied results
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.
124207343
INADMISSIBILITY OF THE BEST EQUIVARIANT ESTIMATORS OF THE VARIANCE-COVARIANCE MATRIX, THE PRECISION MATRIX, AND THE GENERALIZED VARIANCE UNDER ENTROPY LOSS
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 [12] is heavily exploited. AMS 1980 Subject classifications: Primary 62 F 10, Secondary 62 H 99
125654540
On the Equivalence of Confidence Sets Based on Bayesian and Non­Bayesian Procedures*: