Kernel Estimation of the Derivative of the Regression Function Using Repeated-Measurements Data

摘要

In fixed design kernel nonparametic regression, there has been a paucity of results for models which allow for correlated errors. Consider repeated measurements models, applicable in growth curve analysis. It is assumed that the matrix elements may be represented as the product of a scalar variance term and a suitably restricted correlation function. Asympototic expansions of the mean squared error of the Gasser Mueller kernel estimator of an arbitrary pth derivation of g are obtained for two general classes of correlation functions. Consistency and other results based on such expansions are discussed for orders p=1 and p=2. Keywords: Nonparametric regression; Growth curves; Correlated data; Optimum bandwidth; Mean integrated squared error; Gasser Mueller estimator.