Asymptotic Distribution in Moment Structure Analysis Under a Weaker Mode of Convergence and a Weaker Pitman Drift Assumption

• Activity Number: 560
• Type: Contributed
• Date/Time: Wednesday, August 6, 2014 : 2:00 PM to 3:50 PM
• Sponsor: Isolated Statisticians
• Author(s): Hao Wu*+
• Companies: Boston College
• Keywords: moment structure ; asymptotic theory ; Pitman drift ; model misspecification ; structural equation models ; covariance structure

Abstract

The asymptotic distribution of the test statistic under the alternative hypothesis in multivariate analysis under various distribution assumptions and discrepancy functions had long been recognized as a non-central chi square distribution (or a weighted sum thereof) until a normal approximation was proposed as its replacement by Yuan et al (2007). One clear advantage of this normal approximation is that it no longer requires the Pitman drift assumption as usually assumed in the development of the traditional noncentral chi square approximation. This assumption requires that the size of population misspecification drifts with sample size and is therefore considered impractical. In this paper, we prove that the noncentral chi square approximation is valid as long as the sample size is large enough and the model misspecification is small enough, with no Pitman drift needed. This is proved within two new methodological frameworks: first, a weaker assumption than Pitman drift is introduced where population misspecification converges to 0 as a process independent of sample size; second, the asymptotic distribution is allowed to vary with sample size and misspecification.