Bootstrap Tests and Confidence Regions for Functions of a Covariance Matrix

Beran, Rudolf; Srivastava, M. S.

doi:10.1214/aos/1176346579

Cited by 234 publications

(170 citation statements)

References 11 publications

Supporting

Mentioning

156

Contrasting

Order By: Relevance

“…The bootstrap distribution, as usual, converges (weakly) to the (random) conditional distribution of IZ + Z'l -IZ'I given Z'. This phenomenon was first observed in a more realistic context by Beran and Srivastava (1985). Diimbgen (1993) …”

Section: Examples Of Bootstrap Failurementioning

confidence: 63%

Resampling Fewer Than n Observations: Gains, Losses, and Remedies for Losses

Bickel

Götze

Zwet

2011

Selected Works of Willem Van Zwet

236

217

View full text Add to dashboard Cite

Abstract:We discuss a number of resampling schemes in which m = o(n) observations are resampled. We review nonparametric bootstrap failure and give results old and new on how the m out of n with replacement and without replacement bootstraps work. We extend work of Bickel and Yahav (1988) to show that m out of n bootstraps can be made second order correct , if the usual nonparametric bootstrap is correct and study how these extrapolation techniques work when the nonparametric bootstrap does not.

show abstract

Section: Examples Of Bootstrap Failurementioning

confidence: 63%

Resampling Fewer Than n Observations: Gains, Losses, and Remedies for Losses

Bickel

Götze

Zwet

2011

Selected Works of Willem Van Zwet

236

217

View full text Add to dashboard Cite

show abstract

“…The motivation behind (1) is to take account of the covariance structure implied by the null hypothesis. If d is constructed in this way then the bootstrap test has the desired asymptotic level (Beran & Srivastava, 1985), that is, the probability of type I error converges to the nominal level a as N tends to infinity. Let Y* = {yl, ... , yN} be a random sample of size N from G, called the bootstrap sample.…”

Section: Bootstrap Testmentioning

confidence: 99%

Efficient Bootstrap Tests for the Goodness of Fit in Covariance Structure Analysis

Ichikawa

Konishi

2001

Behaviormetrika

View full text Add to dashboard Cite

“…That is, the level of the bootstrap test is expected to converge to the nominal level more rapidly than does the level of the asymptotic test. Beran and Srivastava (1985) proved that if model restrictions are taken into account in designing the resampling algorithm, then the bootstrap critical values for various test statistics used for testing structural hypotheses about the population covariance matrix have the desired asymptotic levels.…”

Section: Testing Goodness Of Fit In Factor Analysismentioning

confidence: 99%

Bootstrap Tests for the Goodness of Fit in Factor Analysis

Ichikawa

Konishi

1997

Behaviormetrika

View full text Add to dashboard Cite

Asymptotic robustness studies have shown that normal theory based test statistic for the goodness of fit in factor analysis and related structural models retains its asymptotic chi-square distribution under the null hypothesis if the latent vector vari ables are independently distributed.The asymptotic test, however, may not be robust against the independence assumption, as suggested by a recent Monte Carlo study. A Monte Carlo experiment is conducted to compare the asymptotic and the bootstrap tests across 4 exploratory factor analysis models, 5 sample sizes and 6 distributional condi tions ; in some of these conditions the common factors and the unique factors are taken to be dependent.Results of a simulation study indicate that the asymptotic (bootstrap) test rejects (accepts) the null hypothesis too often than expected from nominal levels of tests when the common factors and the unique factors are mutually independent. When they are just uncorrelated the asymptotic test completely broke down, while the boot strap test performed much better, though it rejected the null hypothesis too often

show abstract

Bootstrap Tests and Confidence Regions for Functions of a Covariance Matrix

Cited by 234 publications

References 11 publications

Resampling Fewer Than n Observations: Gains, Losses, and Remedies for Losses

Resampling Fewer Than n Observations: Gains, Losses, and Remedies for Losses

Efficient Bootstrap Tests for the Goodness of Fit in Covariance Structure Analysis

Bootstrap Tests for the Goodness of Fit in Factor Analysis

Contact Info

Product

Resources

About