Two step estimations for a single-index varying-coefficient model with longitudinal data
In this paper, a two-step estimation procedure is proposed to improve the estimation efficiency of the index coefficients in a single-index varying-coefficient model with longitudinal data. In the first step, initial estimators are produced by ignoring the possible correlations between repeated measures. Based on the modified Cholesky decomposition, the least squares technique is applied for estimating the autoregressive coefficients and the innovation variance, and then obtaining the estimated within-subject covariance matrix. In the second step, centralized generalized estimating equations are built to generate more efficient estimators of the index coefficients. Based on the estimated index coefficients, estimators of the unknown functions are obtained by employing a weighted least squares approach. Simulation studies and an analysis of real progesterone data are presented to demonstrate the efficiency of the estimators.
scientific article; zbMATH DE number 6945910
scientific article