Multivariate Regression with Errors in Variables: Issues on Asymptotic Robustness
Estimation and testing of functional or structural multivariate regression with errors in variables, with possibly unbalanced design for replicates, and not necessarily normal data, is developed using only the sample cross-product moments of the data. We give conditions under which normal theory standard errors and an asymptotic chi-square goodness-of-fit test statistic retain their validity despite non-normality of constituents of the model. Assymptotic optimality for a subvector of parameter estimates is also investigated. The results developed apply to methods that are widely available in standard software for structural equation models, such as LISREL or EQS.
KeywordsFunctional Model Normality Assumption Covariance Structure Analysis Moment Structure Linear Latent Variable Model
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