Tests for standardized generalized variances of multivariate normal populations of possibly different dimensions

SenGupta, Ashis

doi:10.1016/0047-259x(87)90153-9

Cited by 43 publications

(27 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Likelihood ratio tests (LRTs) for SGVs in one or several different-dimensional multivariate normal populations and the exact, in terms of Pincherle's H-function, and asymptotic distributions of some of these test statistics have been given by SenGupta [29]. A multivariate version of Hartley's F max statistic that provides a shortcut test for homogeneity of variances in the univariate case may be based on SGVs.…”

Section: Advances In Theorymentioning

confidence: 99%

See 1 more Smart Citation

Generalized Variance

Gupta¹

2005

Encyclopedia of Statistical Sciences

View full text Add to dashboard Cite

Generalized variance (GV), proposed by Wilks, is an one‐dimensional measure of multidimensional scatter. It plays an important role in both theoretical and applied research. GV has been extended to Standardized GV (SGV) to enable comparison of scatters in differing dimensions. Interesting results on the distribution, estimation, and testing of GVs and SGVs have been emerging. Also, these measures have been finding novel applications in a variety of applied problems, ranging from such age‐old areas as agriculture and sample surveys to the modern developments in signal processing and Bioinformatics.

show abstract

Section: Advances In Theorymentioning

confidence: 99%

“…We will denote the population and sample GVs by | | and |S| respectively. The standardized GV (SGV) [29,30] of X is the positive pth root of GV. GV has several interesting interpretations [1].…”

Section: Introductionmentioning

confidence: 99%

Generalized Variance

Gupta¹

2005

Encyclopedia of Statistical Sciences

View full text Add to dashboard Cite

show abstract

“…For a p-variate distribution with covariance matrix , the standardized generalized variance is defined as | | 1/p . The concept has been first introduced by SenGupta [23] and recently revisited by Peña and Rodríguez [20] under the name "effective variance".…”

Section: Introductionmentioning

confidence: 99%

UMVU estimation of the ratio of powers of normal generalized variances under correlation

Iliopoulos

2008

Journal of Multivariate Analysis

View full text Add to dashboard Cite

We consider estimation of the ratio of arbitrary powers of two normal generalized variances based on two correlated random samples. First, the result of Iliopoulos [Decision theoretic estimation of the ratio of variances in a bivariate normal distribution, Ann. Inst. Statist. Math. 53 (2001) 436-446] on UMVU estimation of the ratio of variances in a bivariate normal distribution is extended to the case of the ratio of any powers of the two variances. Motivated by these estimators' forms we derive the UMVU estimator in the multivariate case. We show that it is proportional to the ratio of the corresponding powers of the two sample generalized variances multiplied by a function of the sample canonical correlations. The mean squared errors of the derived UMVU estimator and the maximum likelihood estimator are compared via simulation for some special cases.

show abstract

“…It gives an overall intuitive idea about the scatter of the multidimensional points. SenGupta (1987) has studied the test for standardized generalized variance when the underlying distribution is multivariate normal with an arbitrary covariance matrix. Bhandary (1996) considered the test for generalized variance in signal processing for white noise and colored noise models.…”

Section: Introductionmentioning

confidence: 99%