Fitting Covariance Structure Models With Arbitrary Observed Distributions

Strong Convergence of the Asymptotically Distribution-Free Estimator

Bibliographic Data

ID12424900
AuthorsTenko Raykov (0000-0002-8911-5116, Michigan State University, corresponding author), Spiridon Penev (0000-0002-3669-0010, UNSW Sydney), Bingsheng Zhang (0009-0006-8519-0713, StataCorp LLC)
Year2025
Volume33
Issue1
Pages32-38
Publication date2025-09-25
Open AccessYes
TypeARTICLE
VenueStructural Equation Modeling: A Multidisciplinary Journal (JOURNAL)
Journal identifiersISSN: 1070-5511 • E-ISSN: 1532-8007
PublisherTaylor & Francis (PUBLISHER • GB)
DOI10.1080/10705511.2025.2556028
OpenAlexW4414499488
LanguageEN
References cited14

The large-sample behavior of the asymptotically distribution-free estimator in covariance structure analysis is studied. It is shown that with increasing sample size and under suitable conditions, the estimator almost surely converges to the true parameter value. This strong convergence (i) represents numerical convergence with probability 1 of the resulting estimates of model parameters to their respective population values, as well as (ii) is stronger than the consistency and convergence in distribution of a parameter estimator, thus implying the latter two types of large-sample behavior. The demonstrated asymptotic convergence of the asymptotically distribution-free estimator for covariance structure models is illustrated on data

Statistical Distribution Estimation and Applications · Statistical Methods and Bayesian Inference · Statistical Methods and Inference

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Open DOIOpen Access