Nonparametric Regression Method for Growth Curve Model
|School||East China Normal University|
|Course||Probability Theory and Mathematical Statistics|
|Keywords||Growth curve model Parametric method Nonparametric approach Local polynomial smoother Ideal choice of bandwidth|
The growth curve model first introduced by Wishart (1938) is a generalization of the multivariate analysis of variance model and is useful especially for investigating growth problem in modern medicine, agricultural and so on. In the model it is frequently assumed that the growth curve is a polynomial in time. In practice, researchers mainly use higher-order polynomials to obtain more precise estimates. While this approach has been widely used, it suffers from some drawbacks, such as model can easily affected by outliers and the polynomial hypothesis may much strong in practice. So in this paper we first proposed nonparametric approach, local polynomial smoother, instead of parametric method for estimation in growth curve model.In the first chapter we give a brief description of the growth curve model and its drawbacks. And we also give a brief introduction to the estimating method of univariate nonparametric regression model, it includes the spline approach, the orthogonal series approach and the local modeling approach. In the second chapter we define the Nonpara-metric Growth Curve Model, and give its nonparametric estimation. Also, the properties of the nonparametric estimation discussed in this chapter. Reference the method which was proposed by Fan and Gijbels in1996, we discuss the large sample character of local polynomial estimate in chapter3. It is an important aspect that how to choose good bandwidth for nonparametric regression, so the ideal theoretical choice of a local band-width is also discussed in details in the fourth chapter. In the last chapter simulation study are presented and it aims to compare the parametric and nonparametric approach. Prom the simulation study, we can clearly see that the performance of nonparametric approach is much better than parametric technique.