Distributions of characteristic roots in multivariate analysis Part II. Non-Null Distribution (Q4157835)

scientific article; zbMATH DE number 3589596

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English	Distributions of characteristic roots in multivariate analysis Part II. Non-Null Distribution	scientific article; zbMATH DE number 3589596

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scholarly article

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title

Distributions of characteristic roots in multivariate analysis Part II. Non-Null Distribution (English)

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author

K. C. S. Pillai

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publication date

1977

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MaRDI profile type

Publication

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full work available at URL

https://doi.org/10.2307/3315084

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cites work

On the Noncentral Distributions of the Second Largest Roots of Three Matrices in Multivariate Analysis

0 references

An Asymptotic Expansion for the Distribution of the Latent Roots of the Estimated Covariance Matrix

0 references

Some Extensions of the Wishart Distribution

0 references

The Non-Central Wishart Distribution and Certain Problems of Multivariate Statistics

0 references

Q5795318

0 references

Q3255781

0 references

Asymptotic Theory for Principal Component Analysis

0 references

Monotonicity of the Power Functions of Some Tests of Independence between Two Sets of Variates

0 references

Some Optimum Confidence Bounds for Roots of Determinantal Equations

0 references

Q3844714

0 references

Q3290189

0 references

On the exact distribution of the ratio of (p×p) Generalized sample variance to any of its principal minors

0 references

The Distribution of the Generalized Variance

0 references

On the exact distribution of the ratio of two independent generalized sample variances of the same or different orders

0 references

Q5663248

0 references

Q5658992

0 references

Q4757974

0 references

Properties of sufficiency and statistical tests

0 references

Q5767935

0 references

Q5777633

0 references

The General Canonical Correlation Distribution

0 references

An Asymptotic Expansion for the Distribution of the Eigenvalues of a 3 by 3 Wishart Matrix

0 references

An identity involving partitional generalized binomial coefficients

0 references

A GENERAL DISTRIBUTION THEORY FOR A CLASS OF LIKELIHOOD CRITERIA

0 references

Asymptotic formulae for the distributions of some criteria for tests of equality of covariance matrices

0 references

Q4137936

0 references

Maximization of an integral of a matrix function and asymptotic expansions of distributions of latent roots of two matrices

0 references

Tables for the extreme roots of the wishart matrix

0 references

On the General Canonical Correlation Distribution

0 references

Some Non-Central Distribution Problems in Multivariate Analysis

0 references

Partial differential equations for hypergeometric functions of two argument matrices

0 references

Asymptotic expansions for distributions of latent roots in multivariate analysis

0 references

Distribution of the Determinant of the Sum of Products Matrix in the Non‐Central Linear Case

0 references

0 references

0 references

0 references

0 references

On the Exact Distributions of the Likelihood Ratio Criteria for Testing Linear Hypotheses About Regression Coefficients

0 references

On the Exact Distributions of Likelihood Ratio Criteria for Testing Independence of Sets of Variates Under the Null Hypothesis

0 references

On the Exact Distributions of the Criterion $W$ for Testing Sphericity in a $p$-Variate Normal Distribution

0 references

Q5587374

0 references

Properties of Power Functions of Some Tests Concerning Dispersion Matrices of Multivariate Normal Distributions

0 references

Q3214160

0 references

On the Null Distribution of the Sum of the Roots of a Multivariate Beta Distribution

0 references

Percentile approximations for a class of likelihood ratio criteria

0 references

On the Marginal Distributions of the Latent Roots of the Multivariate Beta Matrix

0 references

On the distributions of the latent roots and traces of certain random matrices

0 references

On the ratios of the individual latent roots to the trace of a Wishart matrix

0 references

Q5806233

0 references

Q5595935

0 references

Distributions Connected with a Multivariate Beta Statistic

0 references

On the Expected Values of the Elementary Symmetric Functions of a Noncentral Wishart Matrix

0 references

Q5180724

0 references

A monotonicity property of the power functions of some invariant tests for MANOVA

0 references

THE SAMPLING DISTRIBUTION OF SOME STATISTICS OBTAINED FROM NON‐LINEAR EQUATIONS

0 references

Q5658989

0 references

Q5610137

0 references

Asymptotic formulas for the distributions of the determinant and the trace of a noncentral beta matrix

0 references

Q5540059

0 references

Q5664685

0 references

Bayesian Estimation in Multivariate Analysis

0 references

On Tests of the Equality of Two Covariance Matrices

0 references

On the Sampling Theory of Roots of Determinantal Equations

0 references

Q5781676

0 references

A Note on the Sphericity Test

0 references

Equality of More Than Two Variances and of More Than Two Dispersion Matrices Against Certain Alternatives

0 references

Some distance properties of latent root and vector methods used in multivariate analysis

0 references

Noncentral Distribution of Wilks' Statistic in Manova

0 references

Latent roots and vectors of a Wishart matrix

0 references

Percentage points of the extreme roots of a Wishart matrix

0 references

Q4042605

0 references

On the distribution of a quadratic form in a multivariate normal sample

0 references

On the distribution of the maximum latent root of a positive definite symmetric random matrix

0 references

On the distribution of the latent roots of a positive definite random symmetric matrix. I

0 references

On the derivation of the asymptotic distribution of the generalized Hotelling's $T^2_0$

0 references

Charts of Some Upper Percentage Points of the Distribution of the Largest Characteristic Root

0 references

Bessel functions of matrix argument

0 references

Generalized Asymptotic Expansions of Cornish-Fisher Type

0 references

The Generalization of Student's Ratio

0 references

RELATIONS BETWEEN TWO SETS OF VARIATES

0 references

Q5823902

0 references

ON THE DISTRIBUTION OF ROOTS OF CERTAIN DETERMINANTAL EQUATIONS

0 references

ON GENERALIZED ANALYSIS OF VARIANCE. (I)

0 references

An algebraic derivation of the distribution of rectangular coordinates

0 references

On the Limiting Distribution of Roots of a Determinantal Equation

0 references

ON THE LIMITING DISTRIBUTION OF THE CANONICAL CORRELATIONS

0 references

Asymptotic Formulae for the Distribution of Hotelling's Generalized $T_0^2$ Statistic. II

0 references

Q3291977

0 references

A comparison of the powers of two multivariate analysis of variance tests

0 references

Q5737486

0 references

Q5343364

0 references

Normal Multivariate Analysis and the Orthogonal Group

0 references

The non-central Wishart distribution

0 references

A generating function for averages over the orthogonal group

0 references

The Distribution of the Latent Roots of the Covariance Matrix

0 references

Zonal polynomials of the real positive definite symmetric matrices

0 references

Distributions of Matrix Variates and Latent Roots Derived from Normal Samples

0 references

Calculation of Zonal Polynomial Coefficients by Use of the Laplace-Beltrami Operator

0 references

Q5826110

0 references

The distribution of a statistic used for testing sphericity of normal distributions

0 references

Q5661032

0 references

Some Results on the Distribution of Two Random Matrices Used in Classification Procedures

0 references

Decomposition of the Multivariate Beta Distribution with Applications

0 references

Distribution of the Likelihood Ratio for Testing Multivariate Linear Hypotheses

0 references

On the Mutual Independence of Certain Statistics

0 references

Simultaneous confidence bounds on the departures from a particular kind of multicollinearity

0 references

A note on the confidence bounds for the characteristic roots of dispersion matrices of normal variates

0 references

Some Results on the Non-Central Multivariate Beta Distribution and Moments of Traces of Two Matrices

0 references

On Certain Distribution Problems Based on Positive Definite Quadratic Functions in Normal Vectors

0 references

On the Moments of the Trace of a Matrix and Approximations to Its Non- Central Distribution

0 references

On the moments of traces of two matrices in multivariate analysis

0 references

On the Non-Central Distributions of Two Test Criteria in Multivariate Analysis of Variance

0 references

On the Moments of Elementary Symmetric Functions of the Roots of Two Matrices and Approximations to a Distribution

0 references

Q5639204

0 references

Q5653458

0 references

On the exact finite series distribution of the smallest or the largest root of matrices in three situations

0 references

Admissible Bayes Character of $T^2-, R^2-$, and Other Fully Invariant Tests for Classical Multivariate Normal Problems

0 references

On the distribution of a statistic used for testing a covariance matrix

0 references

A NOTE ON CONFIDENCE BOUNDS FOR CERTAIN RATIOS OF CHARACTERISTIC ROOTS OF COVARIANCE MATRICES

0 references

On the exact distributions of the extreme roots of the Wishart and MANOVA matrices

0 references

Exact joint distributions of any few ordered roots of a class of random matrices

0 references

On the exact distribution of the smallest root of the Wishart matrix using zonal polynomials

0 references

Simultaneous tests for equality of latent roots against certain alternatives. I

0 references

Simultaneous tests for equality of latent roots against certain alternatives. II

0 references

Some recent developments on complex multivariate distributions

0 references

Bartlett Decomposition and Wishart Distribution

0 references

The Non-Central Multivariate Beta Distribution

0 references

Q5332941

0 references

Q5580806

0 references

A GENERALIZATION OF FISHER'S z TEST

0 references

TESTS OF SIGNIFICANCE FOR THE LATENT ROOTS OF COVARIANCE AND CORRELATION MATRICES

0 references

On Testing a Set of Correlation Coefficients for Equality

0 references

Asymptotic formulae for the distribution of a multivariate test statistic: Power comparisons of certain multivariate tests

0 references

Q3262608

0 references

Asymptotic Expansions for Distributions of the Roots of Two Matrices from Classical and Complex Gaussian Populations

0 references

Latent vectors of random symmetric matrices

0 references

Distribution of a Product and the Structural Set Up of Densities

0 references

Q5610478

0 references

On the distribution of the likelihood ratio criterion for testing linear hypotheses on regression coefficients

0 references

Q5627512

0 references

The exact non-central distribution of the generalized variance

0 references

Q5658991

0 references

A few remarks about some recent articles on the exact distributions of multivariate test criteria. I

0 references

Q5184309

0 references

Q4221096

0 references

Q5835642

0 references

Some Bounds on the Distribution Functions of the Largest and Smallest Roots of Normal Determinantal Equations

0 references

The Moments of Elementary Symmetric Functions of the Roots of a Matrix in Multivariate Analysis

0 references

On Elementary Symmetric Functions of the Roots of a Multivariate Matrix: Distributions

0 references

A comparison of tests of the Wilks-Lawley hypothesis in multivariate analysis

0 references

On a Property of a Test for the Equality of Two Normal Dispersion Matrices Against One-sided Alternatives

0 references

On the Distribution of the Characteristic Roots of Normal Second-Moment Matrices

0 references

Q4127200

0 references

A Class of Tests with Monotone Power Functions for Two Problems in Multivariate Statistical Analysis

0 references

On Confidence Bounds Associated with Multivariate Analysis of Variance and Non-Independence Between Two Sets of Variates

0 references

A note on the union-intersection character of some MANOVA procedures

0 references

Systems of Partial Differential Equations for Hypergeometric Functions of Matrix Argument

0 references

Asymptotic Distributions of Some Multivariate Tests

0 references

On the Test of Independence Between Two Sets of Variates

0 references

On the calculation of generalized binomial coefficients

0 references

Asymptotic expansions for the joint and marginal distributions of the latent roots of the covariance matrix

0 references

Forms for the distribution of ss ilkptxcxtt statistic for bivariate sphericity

0 references

The distribution of the sphericity test criterion

0 references

Distribution of the likelihood ratio criterion for testing a hypothesis specifying a covariance matrix

0 references

THE APPLICATION OF THE MOMENT FUNCTION IN THE STUDY OF DISTRIBUTION LAWS IN STATISTICS

0 references

Limiting Distribution of a Root of a Determinantal Equation

0 references

Distribution of the Sum of Roots of a Determinantal Equation under a Certain Condition

0 references

Q5823901

0 references

On Multivariate Distribution Theory

0 references

Multivariate Beta Distributions and Independence Properties of the Wishart Distribution

0 references

On the monotonicity of the power functions of tests based on traces of multivariate beta matrices

0 references

Q5586889

0 references

Q5670064

0 references

Some New Test Criteria in Multivariate Analysis

0 references

ON THE DISTRIBUTION OF THE LARGEST OR THE SMALLEST ROOT OF A MATRIX IN MULTIVARIATE ANALYSIS

0 references

Some Results Useful in Multivariate Analysis

0 references

Q3242484

0 references

On the Moments of the Trace of a Matrix and Approximations to its Distribution

0 references

On the Distribution of the Largest of Seven Roots of a Matrix in Multivariate Analysis

0 references

On the Moments of Elementary Symmetric Functions of the Roots of Two Matrices

0 references

On the distribution of the largest characteristic root of a matrix in multivariate analysis

0 references

On elementary symmetric functions of the roots of two matrices in multivariate analysis

0 references

On the Distribution of the Largest Root of a Matrix in Multivariate Analysis

0 references

Upper percentage points of the largest root of a matrix in multivariate analysis

0 references

On the distribution of the second elementary symmetric function of the roots of a matrix

0 references

On the Moment Generating Function of Pillai's $V^{(s)}$ Criterion

0 references

On the Non-central Distribution of the Second Elementary Symmetric Function of the Roots of a Matrix

0 references

Power comparisons of tests of two multivariate hypotheses based on individual characteristic roots

0 references

On the exact distribution of Wilks's criterion

0 references

On the moments of elementary symmetric functions of the roots of two matrices

0 references

Non-central distributions of the largest latent roots of three matrices in multivariate analysis

0 references

Q5632003

0 references

Power Comparisons of Tests of Equality of Two Covariance Matrices Based on Individual Characteristic Roots

0 references

An approximation to the C. D. F. of the largest root of a covariance matrix

0 references

Q5639205

0 references

On the distribution of hotelling's trace and power comparisons

0 references

The distribution of the characteristic roots of $S_1S^{-1}_2$ under violations

0 references

Exact robustness studies of tests of two multivariate hypotheses based on four criteria and their distribution problems under violations

0 references

Power of the likelihood-ratio test of the general linear hypothesis in multivariate analysis

0 references

A generalized multivariate analysis of variance model useful especially for growth curve problems

0 references

TESTS OF SIGNIFICANCE IN MULTIVARIATE ANALYSIS

0 references

Q5813601

0 references

Some Statistical Methods for Comparison of Growth Curves

0 references

0 references

0 references

0 references

0 references

0 references

On a Heuristic Method of Test Construction and its use in Multivariate Analysis

0 references

Simultaneous Confidence Interval Estimation

0 references

Some Further Results in Simultaneous Confidence Interval Estimation

0 references

FURTHER CONTRIBUTIONS TO MULTIVARIATE CONFIDENCE BOUNDS

0 references

On the Monotonic Character of the Power Functions of Two Multivariate Tests

0 references

Q5725137

0 references

Q5663251

0 references

Expectation of elementary symmetric functions of a Wishart matrix

0 references

Exact distributions of Wilks's likelihood ratio criterion

0 references

Upper percentage points of the smallest root of the MANOVA matrix

0 references

Tables for the power function of box's two sided test for testing hypothesis ∑= I the bivariate case

0 references

On the distributions of the ratios of the extreme roots to the trace of the Wishart matrix

0 references

Exact percentage points of the dsitribtuion of the race of a multivariate beta matrix

0 references

Distribution Theory of a Positive Definite Quadratic Form with Matrix Argument

0 references

Proof of conjectures about the expected values of the elementary symmetric functions of a noncentral Wishart matrix

0 references

Note on the utilization of the generalized student ratio in the analysis of variance or dispersion

0 references

An Asymptotic Expansion of the Non-Null Distribution of Hotelling's Generalized $T_0^2$-Statistic

0 references

On the Distribution of two Random Matrices used in Classification Procedures

0 references

0 references

0 references

0 references

0 references

0 references

Unbiasedness of Some Test Criteria for the Equality of One or Two Covariance Matrices

0 references

Asymptotic non-null distributions of the likelihood ratio criteria for covariance matrix under local alternatives

0 references

Asymptotic Expansions of the Distributions of the Likelihood Ratio Criteria for Covariance Matrix

0 references

Asymptotic Expansions of the Non-Null Distributions of the Likelihood Ratio Criteria for Multivariate Linear Hypothesis and Independence

0 references

Note on Some Formulas for Weighted Sums of Zonal Polynomials

0 references

Asymptotic expansion of the distribution of the generalized variance for noncentral Wishart matrix, when $\Omega= O(n)$

0 references

Locally Best Invariant Test for Sphericity and the Limiting Distributions

0 references

Derivatives of the characteristic root of a synmetric or a hermitian matrix with two applications in multivariate analysis

0 references

Asymptotic formulas for the distributions of two trace statistics for testing the independence under fixed alternative

0 references

On the Distribution of the Latent Vectors for Principal Component Analysis

0 references

On the Distribution of the Largest Latent Root and the Corresponding Latent Vector for Principal Component Analysis

0 references

On the Distribution of the Largest Latent Root of the Covariance Matrix

0 references

Distribution of the Largest Latent Root and the Smallest Latent Root of the Generalized $B$ Statistic and $F$ Statistic in Multivariate Analysis

0 references

Joint Distribution of the Extreme Roots of a Covariance Matrix

0 references

APPROXIMATION FOR THE DISTRIBUTION OF THE LARGEST LATENT ROOT OF A WISHART MATRIX*<sup>,</sup><sup>1</sup>

0 references

Estimation of dispersion parameters

0 references

Bayesian estimation of latent roots and vectors with special reference to the bivariate normal distribution

0 references

Q5620265

0 references

Central and noncentral distributions of Wilks' statistic in MANOVA as mixtures of incomplete beta functions

0 references

The Distributions of Some Test Criteria in Multivariate Analysis

0 references

Q5664689

0 references

Q5664688

0 references

Q5601206

0 references

A Note on Wilks' Internal Scatter

0 references

Computation of the null distribution of the largest or smallest latent roots of a beta matrix

0 references

On the Distribution of Wilks' Statistic for Testing the Independence of Several Groups of Variates

0 references

Q5686814

0 references

Q5180723

0 references

Q5820913

0 references

Random Orthogonal Transformations and their use in Some Classical Distribution Problems in Multivariate Analysis

0 references

CERTAIN GENERALIZATIONS IN THE ANALYSIS OF VARIANCE

0 references

Moment-generating operators for determinants of product moments in samples from a normal system

0 references

On the Independence of k Sets of Normally Distributed Statistical Variables

0 references

Test Criteria for Statistical Hypotheses Involving Several Variables

0 references

Sample Criteria for Testing Equality of Means, Equality of Variances, and Equality of Covariances in a Normal Multivariate Distribution

0 references

Q3270898

0 references

published in

The Canadian Journal of Statistics

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Identifiers

zbMATH Open document ID

0378.62056

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DOI

10.2307/3315084

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Mathematics Subject Classification ID

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Sitelinks

Mathematics(1 entry)

mardi Publication:4157835