Singular Wishart and multivariate beta distributions (2003)
In this article, we consider the case when the number of observations n is less than the dimension p of the random vectors which are assumed to be independent and identically distributed as normal...
Minimax Multivariate Empirical Bayes Estimators under Multicollinearity (2002)
Srivastava, M. S., Kubokawa, Tatsuya
In this paper we consider the problem of estimating the matrix of regression coefficients in a multivariate linear regression model in which the design matrix is near singular. Under the assumption...
Estimating the Covariance Matrix : A New Approach (2002)
Kubokawa, Tatsuya, M. S. Srivastava
Former Version: 1999-CF-52
Improved nonnegative estimation of multivariate components of variance (1999)
Kubokawa, T., Srivastava, M. S.
In this paper,we consider a multivariate one-way random effect model with equal replications. We propose nonnegative definite estimators for “between” and “within” components of variance....
Kubokawa, T., Srivastava, M. S.
This paper derives an extended version of the Haff or, more appropriately, Stein-Haff identity for an elliptically contoured distribution (ECD) . This identity is then used to show that the minimax...
Conditional inference for treatment and error in multivariate analysis (1991)
FRASER, D. A. S., GUTTMAN, I., SRIVASTAVA, M. S.
Directional methods of conditional inference are applied to the multivariate analysis of variance. Exact and easily implemented tests are derived for treatment effect, error variance matrix, and...
The asymptotic variance of the interclass correlation coefficient (1991)
KEEN, K. J., SRIVASTAVA, M. S.
In genetics, the term interclass correlation has been used to refer to the parent-offspring and son-daughter correlations within families. Under the assumption of variable family sizes and...
Estimation of the interclass correlation coefficient (1988)
SRIVASTAVA, M. S., KEEN, K. J.
A noniterative method for estimating the interclass correlation coefficient is derived from the technique of weighted sums of squares. The asymptotic variance of this estimator is derived under the...
Estimation of interclass correlations in familial data (1984)
The maximum likelihood estimates of the parent-child interclass correlation and other parameters from familial data when the families have unequal numbers of offspring is given. Also given are two...
An introduction to applied multivariate statistics / M. S. Srivastava and E. M. Carter (1983)
Incluye bibliografía e índice
Optimum procedures for classification and related problems. (1964)
Thesis (Ph. D.)--Dept. of Statistics, Stanford University.
"Comparison of Discrimination Methods for High Dimensional Data"
M. S. Srivastava, Tatsuya Kubokawa
In microarray experiments, the dimension p of the data is very large but there are only few observations N on the subjects/patients. In this article, the problem of classifying a subject into one of...
"Estimating the Covariance Matrix: A New Approach"
Tatsuya Kubokawa, M. S. Srivastava
In this paper, we consider the problem of estimating the covariance matrix and the generalized variance when the observations follow a nonsingular multivariate normal distribution with unknown mean....
"Minimax Empirical Bayes Ridge-Principal Component Regression Estimators"
Tatsuya Kubokawa, M. S. Srivastava
In this paper, we consider the problem of estimating the regression parameters in a multiple linear regression model with design matrix A when the multicollinearity is present. Minimax empirical...
"Prediction in Multivariate Mixed Linear Models"
Tatsuka Kubokawa, M. S. Srivastava
The multivariate mixed linear model or multivariate components of variance model with equal replications is considered.The paper addresses the problem of predicting the sum of the regression mean and...
"Minimax Multivariate Empirical Bayes Estimators under Multicollinearity"
Tatsuya Kubokawa, M. S. Srivastava
In this paper we consider the problem of estimating the matrix of regression coefficients in a multivariate linear regression model in which the design matrix is near singular. Under the assumption...
"Improved Empirical Bayes Ridge Regression Estimators under Multicollinearity"
Tatsuya Kubokawa, M. S. Srivastava
In this paper we consider the problem of estimating the regression parameters in a multiple linear regression model when the multicollinearity is present.Under the assumption of normality, we present...
Kubokawa, Tatsuya, M. S. Srivastava
This paper derives extended versions of 'Stein' and 'Haff' or more appropriately 'Stein-Haff' identities for elliptically contoured distribution (ECD) models. These identities are then used to...
"Estimating Risk and Mean Squared Error Matrix in Stein Estimation"
Tatsuya Kubokawa, M. S. Srivastava
It is well known that the uniformly minimum variance unbiased (UMVU) estimators of the risk and the mean squared error (MSE) matrix proposed in the literature for Stein estimators can take negative...
"Improved Nonnegative Estimation of Multivariate Components of Variance"
M. S. Srivastava, Tatsuya Kubokawa
In this paper, we consider a multivariate one-way random effect model with equal replications. We propose non-negative definite estimators for 'between' and 'within' components of variance. Under the...
"Estimating the Covariance Matrix: A New Approach", June 1999.
Tatsuya Kubokawa, M. S. Srivastava
In this paper, we consider the problem of estimating the covaraince matrix and the generalized variance when the observations follow a nonsingular multivariate normal distribution with unknown mean....
"Prediction in Multivariate Mixed Linear Models with Equal Replications"
Tatsuya Kubokawa, M. S. Srivastava
The multivariate mixed linear model or multivariate components of variance model with equal replications is considered. The paper addresses the problem of predicting the sum of the regression mean...
Robust Improvement in Estimation of a Mean Matrix in an Elliptically Contoured Distribution
Kubokawa, T., Srivastava, M. S.
In estimation of a matrix of regression coefficients in a multivariate linear regression model, this paper shows that minimax and shrinkage estimators under a normal distribution remain robust under...
Purkayastha, S., Srivastava, M. S.
The asymptotic distributions under local alternatives of two test criteria for testing the hypothesis that the characteristic roots of the covariance matrix of an elliptical population, assumed...
Nagao, Hisao, Srivastava, M. S.
The asymptotic distribution of some test criteria for a covariance matrix are derived under local alternatives. Except for the existence of some higher moments, no assumption as to the form of the...
Estimation of the eigenvalues of [Sigma]1[Sigma]2-1
Bilodeau, M., Srivastava, M. S.
In the normal two-sample problem, an invariant test for the hypothesis of the equality of the population covariance matrices, H:[Sigma]1 = [Sigma]2 vs A:[Sigma]1 [not equal to] [Sigma]2, has a power...
Saddlepoint method for obtaining tail probability of Wilks' likelihood ratio test
Srivastava, M. S., Yau, Wai Kwok
Using the saddlepoint method, two explicit approximation formulae are given for the tail probability of Wilks' likelihood ratio criterion. A comparison with the exact probability shows that these...
Stein estimation under elliptical distributions
Srivastava, M. S., Bilodeau, M.
In a subclass of elliptical distributions, Stein estimators are robust in estimating the mean vector and the regression parameters in a linear regression model. Unbiased estimates of bias and risk...
On monotonicity of the modified likelihood ratio test for the equality of two covariances
Srivastava, M. S., Khatri, C. G., Carter, E. M.
For testing the hypothesis of equality of two covariances ([Sigma]1 and [Sigma]2) of two p-dimensional multivariate normal populations, it is shown that the power function of the modified likelihood...
Asymptotic nonnull distributions for tests for reality of a covariance matrix
Carter, E. M., Srivastava, M. S.
In this paper asymptotic nonnull distributions are derived for two statistics used in testing for the reality of the covariance matrix in a complex Gaussian distribution.
Carter, E. M., Srivastava, M. S.
The modified likelihood ratio criterion for testing the homogeneity of variances of p univariate normal populations, and the sphericity test, are both shown in this paper to have a monotone...
Nonnull distribution of likelihood ratio criterion for reality of covariance matrix
Carter, E. M., Khatri, C. G., Srivastava, M. S.
In this paper the distribution of the likelihood ratio test for testing the reality of the covariance matrix of a complex multivariate normal distribution is investigated. Some simplifications in the...
Some probability inequalities connected with Schur functions
Khatri, C. G., Srivastava, M. S.
Bounds for several integrals (tail probabilities, for example) are established by showing that each integral is a Schur function.
A sequential approach to classification: Cost of not knowing the covariance matrix
Sequential classification cost of not knowing covariance average sample size misclassification errors stopping rule
On assessing multivariate normality based on shapiro-wilk W statistic
Shapiro and Wilk's (1965) W statistic has been found to be the best omnibus test for detecting departures from univariate normality. Royston (1983) extends the application of W to testing...
A measure of skewness and kurtosis and a graphical method for assessing multivariate normality
Using principal components, a measure of skewness and kurtosis is developed for multivariate populations. The sample analogues of these measures are proposed as tests of multivariate normality. Also,...
Estimation of the mean vector of a multivariate normal distribution: subspace hypothesis
This paper considers the estimation of the mean vector [theta] of a p-variate normal distribution with unknown covariance matrix [Sigma] when it is suspected that for a pxr known matrix B the...
Minimax multivariate empirical Bayes estimators under multicollinearity
Srivastava, M. S., Kubokawa, T.
In this paper we consider the problem of estimating the matrix of regression coefficients in a multivariate linear regression model in which the design matrix is near singular. Under the assumption...
Estimating the covariance matrix: a new approach
Kubokawa, T., Srivastava, M. S.
In this paper, we consider the problem of estimating the covariance matrix and the generalized variance when the observations follow a nonsingular multivariate normal distribution with unknown mean....
Estimating Risk and the Mean Squared Error Matrix in Stein Estimation
Kubokawa, T., Srivastava, M. S.
It is well known that the uniformly minimum variance unbiased (UMVU) estimators of the risk and the mean squared error (MSE) matrix proposed in the literature for Stein estimators can take negative...
Fixed Width Confidence Region for the Mean of a Multivariate Normal Distribution
Nagao, Hisao, Srivastava, M. S.
Srivastava gave an asymptotically efficient and consistent sequential procedure to obtain a fixed-width confidence region for the mean vector of any p-dimensional random vector with finite second...
Carter, R.A.L., Srivastava, M.S., Srivastava, V.K., Ullah, A.
We first present an unbiased estimator of the MSE matrix of the Stein-rule estimator of the coefficient vector in a normal linear regression model. The Steinrule estimator can be used with both its...