Varying-coefficient mean–covariance regression analysis for longitudinal data

• A new and efficient estimation for longitudinal data varying-coefficient models.
• Two-stage local polynomial smoothing method is used to estimate the unknown varying coefficient functions of marginal mean.
• A model to model the autoregressive coefficients and innovation variances (based on a modified Cholesky decomposition).

By considering within-subject correlation among repeated measures over time, we propose a new and efficient estimation of varying-coefficient models for longitudinal data. Based on a modified Cholesky decomposition, the within-subject covariance matrix is decomposed into a unit triangular matrix involving generalized autoregressive coefficients and a diagonal matrix involving innovation variances. Local polynomial smoothing method is used to estimate the unknown varying coefficient functions of marginal mean and innovation variances. A method is also developed to estimate the autoregressive coefficients. All the resulting estimators are shown to be consistent and asymptotically normal. The proposed estimator of varying coefficient functions are asymptotically more efficient than the ones which ignore the within-subject correlation structure. Simulations are conducted to demonstrate finite sample behaviors of the proposed estimators, and a real example is given to illustrate the value of the proposed methodology.