Prof Ming-Yen Cheng
In semivarying coefficient modeling of longitudinal/clustered data, usually of primary interest is the parametric component which involves unknown constant coefficients. We first study semiparametric efficiency bound for estimation of the constant coefficients in a general setup. It can be achieved by spline regression provided that the within-cluster covariance matrices are known, which is an unrealistic assumption. Thus, we propose an estimator of the constant coefficients when the covariance matrices are unknown and depend only on the index variable and under the identity link function. After preliminary estimation based on working independence, we estimate the covariance matrices by applying local linear regression to the resultant residuals. Using the covariance matrix estimates, we employ spline regression to obtain our final estimator of the constant coefficients. The proposed estimator achieves the semiparametric efficiency bound under normality assumption, and it has the smallest asymptotic covariance matrix among a class of estimators even when normality is violated. Finite sample performance of our estimator is examined and compared with the working independence estimator and some existing method via simulations and a real data example.