Parameter Estimations And Their Asymptotic Properties In Random Varying-Coefficient Model

Many of statisticians have been interested in longitudinal data because of its wide application. Especially, many of the foreign statisticians are outstanding in longitudinal studies and obtain many of useful results in theory and application. Recently, Hulin, W. and Liang [22] have proposed random varying-coefficient models which is more flexible for longitudinal data. In this model, time-effects and difference of individual are considered by random subject-specific time-varying function. In model analysis, estimation of unknown parameters and its properties are very important, So ,this paper mainly discusses the estimation of parameters and its asymptotic properties in random varying-coefficient model.First ,this paper proposes a new method for estimating random coefficients , namely, we obtain the estimator by fitting a linear mixed-effects models through using B-spline approximation.The resulted estimator is called B-spline estimator.Contrasting to LLME[22], new estimator not only is simple on computer and have locally controlled capability, but also,is smoother on controlling of optimal knots.Moreover, the results show it has good large-sample property, its rate of convergence is Op(N-m/2m+1)Then, about property of the estimator , in practical sampling, frequently, repeated observation is not enough large for many of others factors, So the properties of estimator are important when the numbers of repeated observation are bounded .Therefore, this paper discusses the asymptotic properties of B-spline estimator and LLME estimator in this situation.In this paper, major results are showed as follows: 1) the LLME estimator of random intercept and coefficient functions in...