## Abstract

In semivarying coefficient modeling of longitudinal/clustered data, of primary interest is usually the parametric component which involves unknown constant coefficients. First we study semiparametric efficiency bound for estimation of the constant coefficients in a general setup. It can be achieved by spline regression using the true within-subject covariance matrices, which are often unavailable in reality. Thus we propose an estimator when the covariance matrices are unknown and depend only on the index variable with some specification assumption. To achieve this goal, we estimate the covariance matrices using residuals obtained from a preliminary estimation based on working independence and both spline and local linear regression. Then, using the covariance matrix estimates, we employ spline regression again to obtain our final estimator. It achieves the semiparametric efficiency bound under normality assumption and has the smallest asymptotic covariance matrix among a class of estimators even when normality is violated. Our theoretical results hold either when the number of within-subject observations diverges or when it is uniformly bounded. We also considered nonparametric component estimation. The proposed method is compared with the working independence estimator and some existing method via simulations and application to a real data example.