When is the Student \(t\)-statistic asymptotically standard normal?

From MaRDI portal
Publication:1370237

DOI10.1214/aop/1024404523zbMath0958.60023OpenAlexW2026579437MaRDI QIDQ1370237

Friedrich Götze, David M. Mason, Evarist Giné M.

Publication date: 9 April 2001

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1214/aop/1024404523



Related Items

Almost sure convergence for self-normalized products of sums of partial sums of ρ¯-mixing sequences, Empirical likelihood ratio under infinite second moment for two-sample problems, Further research on limit theorems for self-normalized sums, On the bias and variance of odds ratio, relative risk and false discovery proportion, Central limit theorem and near classical Berry-Esseen rate for self normalized sums in high dimensions, Limit theory for random coefficient autoregressive process under possibly infinite variance error sequence, Moderate deviations for two sample t-statistics, Necessary and sufficient conditions for the asymptotic distribution of the largest entry of a sample correlation matrix, Asymptotics for Self-Normalized Random Products of Sums for Mixing Sequences, Asymptotics for Self-Normalized Random Products of Sums for Mixing Sequences, A PARAMETRIC BOOTSTRAP FOR HEAVY-TAILED DISTRIBUTIONS, Exact rates in complete moment convergence of self-normalized sums for multidimensionally indexed random variables, Weak Convergence of Self-normalized Partial Sums Processes, The Self-normalized Asymptotic Results for Linear Processes, Bootstrapping the Student \(t\)-statistic, The Chow and Robbins Fixed Width Confidence Interval Procedure When the Second Moment Barely Does Not Exist, Convergence and precise asymptotics for series involving self-normalized sums, Optimal-order bounds on the rate of convergence to normality in the multivariate delta method, Self-normalized processes: exponential inequalities, moment bounds and iterated logarithm laws., Exact convergence rate and leading term in central limit theorem for Student's \(t\) statistic., Limit distributions of Studentized means., ASYMPTOTIC PROPERTIES OF SELF-NORMALIZED LINEAR PROCESSES WITH LONG MEMORY, Refined Cramér-type moderate deviation theorems for general self-normalized sums with applications to dependent random variables and winsorized mean, A Self-Normalized Central Limit Theorem for Markov Random Walks, Tail bounds for empirically standardized sums, Almost sure convergence of the largest and smallest eigenvalues of high-dimensional sample correlation matrices, Gnedenko-Raikov's theorem, central limit theory, and the weak law of large numbers, Almost sure central limit theorem for self-normalized partial sums and maxima, Saddlepoint approximation for Student's \(t\)-statistic with no moment conditions, Self-normalization: taming a wild population in a heavy-tailed world, On weak approximations of \(U\)-statistics, A self-normalized central limit theorem for a ρ-mixing stationary sequence, Modified unit root tests with nuisance parameter free asymptotic distributions, Limit theorems for self-normalized linear processes, Coverage accuracy for a mean without third moment, Precise asymptotics of weighted sequences and their applications, Empirical likelihood ratio under infinite covariance matrix of the random vectors, Random deletion does not affect asymptotic normality or quadratic negligibility, Empirical likelihood ratio for two-sample compound Poisson processes under infinite second moment, Further refinement of self-normalized Cramér-type moderate deviations, Exploring functional CLT confidence intervals for a population mean in the domain of attraction of the normal law, On consistency of the least squares estimators in linear errors-in-variables models with infinite variance errors, A kind of complete moment convergence for self-normalized sums, A general result on almost sure central limit theorem for self-normalized sums for mixing sequences, Self-normalized Cramér type moderate deviations for stationary sequences and applications, Domains of attraction of the random vector (X, X 2) and applications, The self-normalized Donsker theorem revisited, Darling-Erdős theorem for self-normalized sums, An almost sure central limit theorem for self-normalized partial sums, An almost sure central limit theorem for self-normalized products of sums of i.i.d. random variables, Precise asymptotics in the deviation probability series of self-normalized sums, An almost sure central limit theorem for self-normalized weighted sums, Towards a universal self-normalized moderate deviation, Process convergence of self-normalized sums of i.i.d. random variables coming from domain of attraction of stable distributions, On the heavy-tailedness of Student's \(t\)-statistic, Quantile coupling inequalities and their applications, Estimation for a longitudinal linear model with measurement errors, Almost sure central limit theory for self-normalized products of sums of partial sums, Functional central limit theorems for self-normalized least squares processes in regression with possibly infinite variance data, Almost sure central limit theorem for self-normalized products of partial sums of negatively associated sequences, Functional central limit theorems for self-normalized partial sums of linear processes, Limit theory for moderate deviations from a unit root under innovations with a possibly infinite variance, Weighted approximations for Studentized \(U\)-statistics, Donsker's theorem for self-normalized partial sums processes, Symmetrization approach to concentration inequalities for empirical processes., Self-normalized Cramér-type large deviations for independent random variables., A note on the normal approximation error for randomly weighted self-normalized sums, Invariance principles for a multivariate Student process in the generalized domain of attraction of the multivariate normal law, Small-time compactness and convergence behavior of deterministically and self-normalised Lévy processes, A central limit theorem for self-normalized sums of a linear process, Precise asymptotes in self-normalized sums of iterated logarithm for multidimensionally indexed random variables, Limit properties for ratios of order statistics from exponentials, Berry-Esseen bounds for self-normalized martingales, Precise asymptotics in the self-normalized law of the iterated logarithm, On necessary and sufficient conditions for the self-normalized central limit theorem, A note on self-normalization for a simple spatial autoregressive model, A nonclassical law of the iterated logarithm for self-normalized partial sums, One-step R-estimation in linear models with stable errors, Invariance principles for adaptive self-normalized partial sums processes., Another look at bootstrapping the Student \(t\)-statistic, Refined self-normalized large deviations for independent random variables, Exponential inequalities for self-normalized martingales, A general law of complete moment convergence for self-normalized sums, A note on unit root tests with heavy-tailed GARCH errors, Testing that marginal sequences of data are not independent via self-normalization, On the quadratic moment of self-normalized sums, Taylor's law, via ratios, for some distributions with infinite mean, Cramér type moderate deviation theorems for self-normalized processes, Asymptotics for self-normalized random products of sums of i.i.d. random variables, Asymptotic Inferences for an AR(1) Model with a Change Point and Possibly Infinite Variance, Precise asymptotics in complete moment convergence for self-normalized sums, Convergence to a self-normalized G-Brownian motion, Central limit theorem for linear processes with infinite variance, Uniform asymptotic normality of self-normalized weighted sums of random variables, The moderate deviation principle for self-normalized sums of sums of i.i.d. random variables, Testing serial non-independence by self-centring and self-normalizing, Random matrix theory for heavy-tailed time series, Limit theorems for ratios of order statistics from uniform distributions, An extension of almost sure central limit theorem for self-normalized products of sums for mixing sequences, A limit theorem for the moment of self-normalized sums, Asymptotic inference for nearly nonstationary AR(1) processes with possibly infinite variance, Two-sided estimates for constants in the Marcinkiewicz inequalities, Asymptotics of the sample coefficient of variation and the sample dispersion, Self-normalized Cramér type moderate deviations for martingales, On weighted approximations in \(D[0,1\) with applications to self-normalized partial sum processes], The asymptotic distribution of self-normalized triangular arrays, On the self-normalized Cramér-type large deviation, Almost sure central limit theorem for self-normalized partial sums of negatively associated random variables, Inference from small and big data sets with error rates, Malliavin Calculus and Self Normalized Sums, Asymptotics for the random coefficient first-order autoregressive model with possibly heavy-tailed innovations, Limiting distributions for eigenvalues of sample correlation matrices from heavy-tailed populations, Quantile inference for moderate deviations from a unit root model with infinite variance, Empirical central limit theorems for exchangeable random variables



Cites Work