Invariant Polynomials and Related Tests

DOI10.1080/01966324.1989.10737254zbMath0718.62103OpenAlexW1992927973WikidataQ58281203 ScholiaQ58281203MaRDI QIDQ5750167

No author found.

Publication date: 1989

Published in: American Journal of Mathematical and Management Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/01966324.1989.10737254

zbMATH Keywords

discriminant analysis Wishart matrix invariant polynomials zonal polynomials multivariate calibration distributions of latent roots robustness studies multinormal populations

Mathematics Subject Classification ID

Multivariate distribution of statistics (62H10) Hypothesis testing in multivariate analysis (62H15)

Cites Work

Distribution of the likelihood ratio criterion for testing a hypothesis specifying a covariance matrix
An Asymptotic Expansion for the Distribution of the Linear Discriminant Function
Distributions of Matrix Variates and Latent Roots Derived from Normal Samples
Some Non-Central Distribution Problems in Multivariate Analysis
The Large-Sample Distribution of the Likelihood Ratio for Testing Composite Hypotheses
ON THE DISTRIBUTION OF ROOTS OF CERTAIN DETERMINANTAL EQUATIONS
On the Sampling Theory of Roots of Determinantal Equations
On the Completely Unbiassed Character of Tests of Independence in Multivariate Normal Systems
On the Distribution of the Characteristic Roots of Normal Second-Moment Matrices
Sample Criteria for Testing Equality of Means, Equality of Variances, and Equality of Covariances in a Normal Multivariate Distribution
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
A solution to the multivariate behrens-fisher problem
Test for independence of two multivariate regression equations with different design matrices
Note on the utilization of the generalized student ratio in the analysis of variance or dispersion
Zonal polynomials of the real positive definite symmetric matrices
Formulas for zonal polynomials
On a result of Roy and Gnanadesikan concerning multivariate variance components
Quadratic forms of a matric-t variate
On the expansion of $C^*_{\rho}(V+I)$ as a sum of zonal polynomials
Some properties of invariant polynomials with matrix arguments and their applications in econometrics
An everywhere convergent series representation of the distribution of Hotelling's generalized $T^ 2_ 0$
Some distribution theory relating to confidence regions in multivariate calibration
Unbiasedness of the likelihood ratio tests for equality of several covariance matrices and equality of several multivariate normal populations
The likelihood ratio criterion and the asymptotic expansion of its distribution
Calculation of zonal polynomials of $3\times 3$ positive definite symmetric matrices
Invariant polynomials with two matrix arguments extending the zonal polynomials: Applications to multivariate distribution theory
Distribution of the canonical correlation matrix
Asymptotic distribution of a generalized Hotelling's T//$0^ 2$ in the doubly noncentral case
Differential operators associated with zonal polynomials. I
On some formulas for weighted sum of invariant polynomials of two matrix arguments
Distributions of some matrix variates and latent roots in multivariate Behrens-Fisher discriminant analysis
On the construction of a class of invariant polynomials in several matrices, extending the zonal polynomials
Eigenfunctions of expected value operators in the Wishart distribution. II
Asymptotic expansions of the non-null distributions of likelihood ratio criteria for covariance matrices
Asymptotic expansions for the joint and marginal distributions of the latent roots of the covariance matrix
Non-null distributions of the likelihood ratio criteria for independence and equality of mean vectors and covariance matrices
On the asymptotic distributions of some statistics used for testing $\Sigma_1=\Sigma_2$
On the derivation of the asymptotic distribution of the generalized Hotelling's $T^2_0$
Asymptotic nonnull distributions of certain test criteria for a covariance matrix
Techniques of multivariate calculation
Further asymptotic formulas for the non-null distributions of three statistics for multivariate linear hypothesis
Asymptotic expansions of the distribution of Bartlett's test and sphericity test under the local alternatives
Asymptotic formulas for the hypergeometric function $_2F_1$ of matrix argument, useful in multivariate analysis
Zonal polynomials: an alternative approach
Latent roots and matrix variates: a review of some asymptotic results
On monotonicity of the modified likelihood ratio test for the equality of two covariances
Asymptotic non-null distributions of two test criteria for equality of covariance matrices under local alternatives
Multivariate Meixner classes of invariant distributions
An identity involving partitional generalized binomial coefficients
Nonnull distributions of two test criteria for independence under local alternatives
Multivariate calculation. Use of the continuous groups
On the distribution of the maximum latent root of a positive definite symmetric random matrix
On the distribution of the latent roots of a positive definite random symmetric matrix. I
Further applications of a differential equation for Hotelling's generalized $\mathbb{T}^2_\circ$
Asymptotic expansions of the non-null distributions of two criteria for the linear hypotheses concerning complex multivariate normal populations
The distribution of the sphericity test criterion
Asymptotic non-null distributions of the likelihood ratio criteria for covariance matrix under local alternatives
On some test criteria for covariance matrix
A theorem on the asymptotic behavior of a multiple integral
Asymptotic non-null distribution of a test of equality of exponential populations
Distribution of likelihood ratio statistic for testing equality of covariance matrices of multivariate Gaussian models
Test of independence between tow sets of variates
Asymptotic Formulae for the Distribution of Hotelling's Generalized $T^2_0$ Statistic
Asymptotic non-null distribution of a test connected with exponential populations
On the distribution of the likelihood ratio test of equality of normal populations
Further results on the trace of a noncentral wishart matrix
Asymptotic non-null distribution for the locally most powerful invariant test for sphericity
Asymptotic distributions of likelihood ratio criteria for testing latent roots and latent vectors of a covariance matrix under an elliptical population
The Exact Distribution of the SUR Estimator
On matric variate-T distribution
EXACT DISTRIBUTION OF CERTAIN GENERAL TEST STATISTICS IN MULTIVARIATE ANALYSIS
The Exact Distribution of the Wald Statistic
Moments of linear discriminant functions and an asymptotic confidence interval for the log odds ratio
On the non-null distributions of test statistics connected with exponential populations
Asymptotic distributions in canonical correlation analysis and other multivariate procedures for nonnormal populations
On the effects of moderate multivariate nonnormality on Wilks's likelihood ratio criterion
The likelihood ratio criterion for a composite hypothesis under a local alternative
Statistical distributions in univariate and multivariate Edgeworth populations
Distributions of Characteristic Roots in Multivariate Analysis Part I. Null Distributions
Distributions of characteristic roots in multivariate analysis Part II. Non-Null Distribution
Orthogonale Polynomsysteme Mit Einer Besonderen Gestalt Der Erzeugenden Funktion
The Asymptotic Noncentral Distribution of Hotelling's Generalized $T_0^2$
An Asymptotic Expansion for the Distribution of the Latent Roots of the Estimated Covariance Matrix
The Relationship Algebra and the Analysis of Variance of a Partially Balanced Incomplete Block Design
A Note on the Sphericity Test
The Distribution of Hotelling's Generalised $T_0^2$
On the Non-Central Distributions of Two Test Criteria in Multivariate Analysis of Variance
On the Distribution of the Largest Latent Root of the Covariance Matrix
Properties of Power Functions of Some Tests Concerning Dispersion Matrices of Multivariate Normal Distributions
Asymptotic Expansions of the Non-Null Distributions of the Likelihood Ratio Criteria for Multivariate Linear Hypothesis and Independence
The Distribution of the Latent Roots of the Covariance Matrix
Asymptotic Expansions of the Distributions of the Likelihood Ratio Criteria for Covariance Matrix
The Distribution of Noncentral Means with Known Covariance
Monotonicity of the Power Functions of Some Tests of Independence between Two Sets of Variates
Joint Distribution of the Extreme Roots of a Covariance Matrix
Measures of multivariate skewness and kurtosis with applications
Asymptotic Distributions of Some Multivariate Tests
Systems of Partial Differential Equations for Hypergeometric Functions of Matrix Argument
Distribution of the Canonical Correlations and Asymptotic Expansions for Distributions of Certain Independence Test Statistics
The distribution of a statistic used for testing sphericity of normal distributions
On the Moment Generating Function of Pillai's $V^{(s)}$ Criterion
Likelihood ratio and associated test criteria
Asymptotic Formulae for the Distribution of Hotelling's Generalized $T_0^2$ Statistic. II
An Asymptotic Expansion of the Non-Null Distribution of Hotelling's Generalized $T_0^2$-Statistic
Locally Best Invariant Test for Sphericity and the Limiting Distributions
A System of Linear Differential Equations for the Distribution of Hotelling's Generalized $T_o^2$
On the Test of Independence Between Two Sets of Variates