Topic
Hotelling's T-squared distribution
About: Hotelling's T-squared distribution is a research topic. Over the lifetime, 297 publications have been published within this topic receiving 21164 citations.
Papers published on a yearly basis
Papers
More filters
Book•
14 Sep 1984
TL;DR: In this article, the distribution of the Mean Vector and the Covariance Matrix and the Generalized T2-Statistic is analyzed. But the distribution is not shown to be independent of sets of Variates.
Abstract: Preface to the Third Edition.Preface to the Second Edition.Preface to the First Edition.1. Introduction.2. The Multivariate Normal Distribution.3. Estimation of the Mean Vector and the Covariance Matrix.4. The Distributions and Uses of Sample Correlation Coefficients.5. The Generalized T2-Statistic.6. Classification of Observations.7. The Distribution of the Sample Covariance Matrix and the Sample Generalized Variance.8. Testing the General Linear Hypothesis: Multivariate Analysis of Variance9. Testing Independence of Sets of Variates.10. Testing Hypotheses of Equality of Covariance Matrices and Equality of Mean Vectors and Covariance Matrices.11. Principal Components.12. Cononical Correlations and Cononical Variables.13. The Distributions of Characteristic Roots and Vectors.14. Factor Analysis.15. Pattern of Dependence Graphical Models.Appendix A: Matrix Theory.Appendix B: Tables.References.Index.
9,693 citations
TL;DR: A scaled Wald statistic is presented, together with an F approximation to its sampling distribution, that is shown to perform well in a range of small sample settings and has the advantage that it reproduces both the statistics and F distributions in those settings where the latter is exact.
Abstract: Restricted maximum likelihood (REML) is now well established as a method for estimating the parameters of the general Gaussian linear model with a structured covariance matrix, in particular for mixed linear models. Conventionally, estimates of precision and inference for fixed effects are based on their asymptotic distribution, which is known to be inadequate for some small-sample problems. In this paper, we present a scaled Wald statistic, together with an F approximation to its sampling distribution, that is shown to perform well in a range of small sample settings. The statistic uses an adjusted estimator of the covariance matrix that has reduced small sample bias. This approach has the advantage that it reproduces both the statistics and F distributions in those settings where the latter is exact, namely for Hotelling T2 type statistics and for analysis of variance F-ratios. The performance of the modified statistics is assessed through simulation studies of four different REML analyses and the methods are illustrated using three examples.
3,862 citations
TL;DR: Applications are provided on the analysis of historical data from the catalytic cracking section of a large petroleum refinery, on the monitoring and diagnosis of a continuous polymerization process and on the Monitoring of an industrial batch process.
702 citations
Book•
15 Dec 1997
TL;DR: In this paper, the authors present a classification of observations into groups based on the properties of Random Vectors and Matrices (RVM) and some properties of random vectors and matrices.
Abstract: Some Properties of Random Vectors and Matrices. The Multivariate Normal Distribution. Hotelling's T -Tests. Multivariate Analysis of Variance. Discriminant Functions for Descriptive Group Separation. Classification of Observations into Groups. Multivariate Regression. Canonical Correlation. Principal Component Analysis. Factor Analysis. Appendices. Bibliography. Index.
439 citations
TL;DR: In this paper, a cross-sectional regression test (CSRT) of the CAPM is developed and its connection to the Hotelling T2 test of multivariate statistical analysis is explored.
427 citations