Likelihood ratio tests for elaborate covariance structures and for MANOVA models with elaborate covariance structures -- a review

DOI10.1007/s41745-022-00300-5OpenAlexW4224267143MaRDI QIDQ6149605

Publication date: 5 March 2024

Published in: Journal of the Indian Institute of Science (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s41745-022-00300-5

zbMATH Keywords

block-diagonal structure exact distribution near-exact distributions inversion methods block compound-symmetry block-circularity block-matrix sphericity block-scalar sphericity double exchangeable structure equality mean vectors hyper-block matrix sphericity

Mathematics Subject Classification ID

Multivariate distribution of statistics (62H10) Asymptotic distribution theory in statistics (62E20) Hypothesis testing in multivariate analysis (62H15) Characterization and structure theory for multivariate probability distributions; copulas (62H05) Research exposition (monographs, survey articles) pertaining to statistics (62-02)

Cites Work

Asymptotic expansion of the nonnull distribution of likelihood ratio statistic for testing multisample sphericity
EXACT DISTRIBUTION OF CERTAIN GENERAL TEST STATISTICS IN MULTIVARIATE ANALYSIS
A Note on the Canonical Correlations From Contingency Tables
Exact distribution of Wilks' l_Vccriterion and its percentage points in the complex case
Saddlepoint approximations for the generalized variance and Wilks' statistic
Some results on the distribution of Wilks's likelihood-ratio criterion
Percentage poits of wilk's L_vccriterion
Numerical inversion of a class of characteristic functions
Exact distribution of sphericity criterion in the complex case and its percentage points
Numerical Inversion of Laplace Transforms Using a Fourier Series Approximation
The Accurate Numerical Inversion of Laplace Transforms
ASYMPTOTIC DISTRIBUTIONS OF THE CANONICAL CORRELATIONS FROM CONTINGENCY TABLES
CERTAIN GENERALIZATIONS IN THE ANALYSIS OF VARIANCE
On the numerical inversion of Laplace transforms
A modification of Talbot's method for the simultaneous approximation of several values of the inverse Laplace transform
Using circulant symmetry to model featureless objects
On two asymptotic normal distributions for the generalized wilks lambda statistic
Applied Multivariate Analysis
Testing sphericity and intraclass covariance structures under a growth curve model in high dimension
A high-dimensional likelihood ratio test for circular symmetric covariance structure
Asymptotic Results of a High Dimensional MANOVA Test and Power Comparison When the Dimension is Large Compared to the Sample Size
A Dimensional CLT for Non-Central Wilks' Lambda in Multivariate Analysis
METHODS OF STATISTICAL ANALYSIS APPROPRIATE FOR k SAMPLES OF TWO VARIABLES
On the Independence of k Sets of Normally Distributed Statistical Variables
Numerical Inversion of Laplace Transforms: An Efficient Improvement to Dubner and Abate's Method
The Multi-Sample Block-Scalar Sphericity Test: Exact and Near-Exact Distributions for Its Likelihood Ratio Test Statistic
Inference for Multivariate Regression Model Based on Synthetic Data Generated Using Plug-in Sampling
High-dimensional MANOVA under weak conditions
On quadratic forms in multivariate generalized hyperbolic random vectors
Simple and efficient adaptive two-sample tests for high-dimensional data
A Simple Two-Sample Test in High Dimensions Based on L²-Norm
Estimating the distribution of a stochastic sum of IID random variables
Diagonal likelihood ratio test for equality of mean vectors in high‐dimensional data
Tests for high-dimensional covariance matrices using the theory ofU-statistics
Tests for High-Dimensional Covariance Matrices
Test for the mean matrix in a Growth Curve model for high dimensions
Inference for Multivariate Regression Model based on synthetic data generated under Fixed-Posterior Predictive Sampling: comparison with Plug-in Sampling
A Two-Sample Test for Equality of Means in High Dimension
Special Functions for Applied Scientists
Growth Curve Modeling
Multivariate Theory for Analyzing High Dimensional Data
Computing the distribution of quadratic forms in normal variables
A Note on the Sphericity Test
A generalized multivariate analysis of variance model useful especially for growth curve problems
Exact distributions of Wilks's likelihood ratio criterion
Numerical Inversion of Laplace Transforms Using Laguerre Functions
On the Exact Distributions of the Criterion $W$ for Testing Sphericity in a $p$-Variate Normal Distribution
On the Exact Distributions of Likelihood Ratio Criteria for Testing Independence of Sets of Variates Under the Null Hypothesis
On the exact distribution of Wilks's criterion
Asymptotic Expansions of the Non-Null Distributions of the Likelihood Ratio Criteria for Multivariate Linear Hypothesis and Independence
Testing and Estimation for a Circular Stationary Model
On the Distributions of the Ratios of the Roots of a Covariance Matrix and Wilks' Criterion for Tests of Three Hypotheses
Unbiasedness of Some Test Criteria for the Equality of One or Two Covariance Matrices
Asymptotic Expansions of the Distributions of the Likelihood Ratio Criteria for Covariance Matrix
The Exact Distribution of Wilks' Criterion
Some Distribution Problems in the Multivariate Complex Gaussian Case
On the Distribution of the Sphericity Test Criterion in Classical and Complex Normal Populations Having Unknown Covariance Matrices
Conditions Under Which Mean Square Ratios in Repeated Measurements Designs Have Exact F-Distributions
A High Dimensional Two Sample Significance Test
Distribution of the Canonical Correlations and Asymptotic Expansions for Distributions of Certain Independence Test Statistics
Percentile approximations for a class of likelihood ratio criteria
Numerical inversion of a characteristic function
On the Exact Distribution of a Class of Multivariate Test Criteria
The Helmert Matrices
The Large-Sample Distribution of the Likelihood Ratio for Testing Composite Hypotheses
THE APPLICATION OF THE MOMENT FUNCTION IN THE STUDY OF DISTRIBUTION LAWS IN STATISTICS
TESTS OF SIGNIFICANCE IN MULTIVARIATE ANALYSIS
Inversion Formulae for the Distribution of Ratios
Testing Compound Symmetry in a Normal Multivariate Distribution
A GENERAL DISTRIBUTION THEORY FOR A CLASS OF LIKELIHOOD CRITERIA
On the Completely Unbiassed Character of Tests of Independence in Multivariate Normal Systems
Note on the inversion theorem
A two sample test in high dimensional data
A new test for sphericity of the covariance matrix for high dimensional data
A general near-exact distribution theory for the most common likelihood ratio test statistics used in multivariate analysis
Central limit theorems for classical likelihood ratio tests for high-dimensional normal distributions
High-dimensional sparse MANOVA
Likelihood ratio tests for covariance matrices of high-dimensional normal distributions
Linear hypothesis testing in high-dimensional one-way MANOVA
Some tests for the covariance matrix with fewer observations than the dimension under non-normality
Asymptotic nonnull distributions for likelihood ratio statistics in the multivariate normal patterned mean and covariance matrix testing problem
The distribution of the product of powers of independent uniform random variables -- a simple but useful tool to address and better understand the structure of some distributions
Numerical inversion of the Laplace transform: a survey and comparison of methods
An asymptotic expansion of the nonnull distribution of Wilks criterion for testing the multivariate linear hypothesis
Statistical tables for multivariate analysis. A handbook with references to applications. Transl. from the German by Peter Wadsack
Near-exact distributions for the independence and sphericity likelihood ratio test statistics
Multivariate analysis of variance with fewer observations than the dimension
Development and comparative study of two near-exact approximations to the distribution of the product of an odd number of independent beta random variables
Study of the quality of several asymptotic and near-exact approximations based on moments for the distribution of the Wilks lambda statistic
Saddlepoint method for obtaining tail probability of Wilk's likelihood ratio test
Analysis of high-dimensional repeated measures designs: the one sample case
The advantage of decomposing elaborate hypotheses on covariance matrices into conditionally independent hypotheses in building near-exact distributions for the test statistics
Corrections to LRT on large-dimensional covariance matrix by RMT
Distribution of LRC for testing sphericity of a complex multivariate Gaussian model
Hypothesis of multisample sphericity
On some properties of positive definite Toeplitz matrices and their possible applications
Unbiasedness of the likelihood ratio tests for equality of several covariance matrices and equality of several multivariate normal populations
Numerical computation of the Fourier transform using Laguerre functions and the fast Fourier transform
A significance test for multisample sphericity
Exact noncentral distributions of Wilks' Lambda and Wilks-Lawley U criteria as mixtures of incomplete beta functions: for three tests
Asymptotic distributions of the likelihood ratio test statistics for covariance structures of the complex multivariate normal distributions
Asymptotic expansions of the non-null distributions of likelihood ratio criteria for covariance matrices
Properties of $I_{MN}$ and $J_{MN}$ approximants and applications to numerical inversion of Laplace transforms and initial value problems
A bibliography on numerical inversion of the Laplace transform and applications
Central and noncentral distributions of Wilks' statistic in MANOVA as mixtures of incomplete beta functions
Non-null distributions of the likelihood ratio criteria for independence and equality of mean vectors and covariance matrices
Asymptotic solutions of the hypergeometric function $_1F_1$ of matrix argument, useful in multivariate analysis
A few remarks about some recent articles on the exact distributions of multivariate test criteria. I
A bibliography on numerical inversion of the Laplace transform and applications: A supplement
Further asymptotic formulas for the non-null distributions of three statistics for multivariate linear hypothesis
Wishart and pseudo-Wishart distributions and some applications to shape theory
The generalized integer gamma distribution -- a basis for distributions in multivariate statistics
Bilinear regression analysis. An introduction
Testing the hypothesis of a block compound symmetric covariance matrix for elliptically contoured distributions
Near-exact distributions for likelihood ratio statistics used in the simultaneous test of conditions on mean vectors and patterns of covariance matrices
Some hypothesis tests for the covariance matrix when the dimension is large compared to the sample size
Laplace approximations for hypergeometric functions with matrix argument
The generalized near-integer Gamma distribution: a basis for `near-exact' approximations to the distribution of statistics which are the product of an odd number of independent Beta random variables
Tests for multivariate analysis of variance in high dimension under non-normality
Distribution and percentage points of LRC for testing multisample compound symmetry in the bivariate and the trivariate cases
Near-exact distributions for the likelihood ratio test statistic of the multi-sample block-matrix sphericity test
Hypothesis tests for high-dimensional covariance structures
On the distribution of the likelihood ratio test of independence for random sample size -- a computational approach
Linear hypothesis testing in high-dimensional one-way MANOVA: a new normal reference approach
Distribution and correlation-free two-sample test of high-dimensional means
Two-sample high dimensional mean test based on prepivots
A more powerful test of equality of high-dimensional two-sample means
Obtaining the exact and near-exact distributions of the likelihood ratio statistic to test circular symmetry through the use of characteristic functions
Generalized hypergeometric functions with applications in statistics and physical sciences
Nonnull distributions of two test criteria for independence under local alternatives
Testing the hypothesis of a doubly exchangeable covariance matrix
Near-exact distributions for certain likelihood ratio test statistics
Finite form representations for Meijer $G$ and Fox $H$ functions. Applied to multivariate likelihood ratio tests using Mathematica, MAXIMA and R
The exact and near-exact distributions of the main likelihood ratio test statistics used in the complex multivariate normal setting
A two-sample test for high-dimensional data with applications to gene-set testing
Some high-dimensional tests for a one-way MANOVA
Near-exact distributions for the sphericity likelihood ratio test statistic
A test for the mean vector with fewer observations than the dimension
Near-exact distributions for the likelihood ratio test statistic to test equality of several variance-covariance matrices in elliptically contoured distributions
An improved Talbot method for numerical Laplace transform inversion
Testing for equality of means, equality of variances, and equality of covariances under restrictions upon the parameter space
The exact distribution of Votaw's criteria
On the distribution of the likelihood ratio criterion for testing linear hypotheses on regression coefficients
Distribution of Wilk's likelihood-ratio criterion in the complex case
The distribution of the sphericity test criterion
On some test criteria for covariance matrix
Gaussian quadrature formulas for the numerica l integration of Bromwich's integral and the inversion of the Laplace transform
Percentage points of Wilk's $L_{mve}$ and $L_{vc}$ criteria
Numerical methods for Laplace transform inversion
Testing high-dimensional covariance matrices under the elliptical distribution and beyond
Tests for a Multiple-Sample Problem in High Dimensions
Methods of Multivariate Analysis
A Test for Multivariate Analysis of Variance in High Dimension
Asymptotic Expansion of the Null Distribution of LR Statistic for Multivariate Linear Hypothesis when the Dimension is Large
Multi-precision Laplace transform inversion
Some Statistical Methods for Comparison of Growth Curves
The Analysis of Experiments on Growth Rate
Some applications of Meijer-G functions to distribution problems in statistics
Some Classification Problems with Multivariate Qualitative Data
Estimation of Time-Response Curves and Their Confidence Bands
Asymptotic Expansions of the Non-Null Distribution of the Likelihood Ratio Criterion for Multisample Sphericity
Computing the exact distribution of a linear combination of generalized logistic random variables and its applications
A Multivariate Two-Sample Mean Test for Small Sample Size and Missing Data
Likelihood Ratio Tests for High‐Dimensional Normal Distributions
Analysis of high-dimensional one group repeated measures designs
The fundamental limit theorems in probability
On the Distribution of the Quotient of Two Chance Variables
Extension of a Theorem by Harald Cramer on the Frequency Distribution of the Quotient of Two Variables
Approximation of the Distribution of the Product of Beta Variables by a Single Beta Variable
Sample Criteria for Testing Equality of Means, Equality of Variances, and Equality of Covariances in a Normal Multivariate Distribution
Computing the exact distribution of the Bartlett's test statistic by numerical inversion of its characteristic function
On the exact computation of the density and of the quantiles of linear combinations of $t$ and $F$ random variables
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item