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Nonparametric Estimation of Standard Errors in Covariance Analysis Using the Infinitesimal Jackknife

Published online by Cambridge University Press:  01 January 2025

Robert I. Jennrich
Robert I. Jennrich*
Affiliation:
University of California at Los Angeles
*
Requests for reprints should be sent to Robert I. Jennrich, Department of Mathematics, University of California, Los Angeles, CA 90095, USA. E-mail: rij@stat.ucla.edu
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Abstract

The infinitesimal jackknife provides a simple general method for estimating standard errors in covariance structure analysis. Beyond its simplicity and generality what makes the infinitesimal jackknife method attractive is that essentially no assumptions are required to produce consistent standard error estimates, not even the requirement that the population sampled has the covariance structure assumed. Commonly used covariance structure analysis software uses parametric methods for estimating parameters and standard errors. When the population sampled has the covariance structure assumed, but fails to have the distributional form assumed, the parameter estimates usually remain consistent, but the standard error estimates do not. This has motivated the introduction of a variety of nonparametric standard error estimates that are consistent when the population sampled fails to have the distributional form assumed. The only distributional assumption these require is that the covariance structure be correctly specified. As noted, even this assumption is not required for the infinitesimal jackknife. The relation between the infinitesimal jackknife and other nonparametric standard error estimators is discussed. An advantage of the infinitesimal jackknife over the jackknife and the bootstrap is that it requires only one analysis to produce standard error estimates rather than one for every jackknife or bootstrap sample.

Keywords

confirmatory factor analysiscovariance structure analysisestimation equationsminimum deviance estimationmisspecified covariance structurenumeric derivativespseudo valuesstructural equation modelingrobust standard errors
Type
Theory and Methods
Information
Psychometrika , Volume 73 , Issue 4 , December 2008 , pp. 579 - 594
Copyright
Copyright © 2008 The Psychometric Society

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