Selection of Loss Function in Covariance Structure Analysis: Case of the Spherical Model

In this paper, we derive the asymptotic properties of estimators obtained from various kinds loss functions in covariance structure analysis. We first show that except for OLS-based have same distribution when dimension matrix, p, is fixed and sample size n tends to infinity. Then, focusing on spherical model, equivalence does not hold both p become larger. Specifically, some lose consistency, even consistent different variances. Among considered, maximum likelihood estimator shows best performance, while less famous invGLS(ub) performs better than commonly used GLS estimator. also demonstrate validity ratio test diagonal models a high-dimensional framework.