The Scalar Response Functional Linear Model And Partial Functional Linear Model With Errors-In-Variables

With the development of science and technology, people collect more intensive data in nowadays which can be approximately regarded as curves. However, due to the multicolinearity of intensive data, the classical regression model is no longer suitable. Therefore, functional linear model is proposed as an extension of linear regression model. Besides, data collected by instrument or human respondent cause the measurement error. For these reason, studying the functional linear model with measurement error is an extension and perfection of regression model which has practical application value.At the beginning of this thesis, i.e. chapter two, introduces the L2 space model of function-al data and the method of dimension reduction with functional principal components analysis (FPCA). Besides, estimating the parameter in the scalar response functional linear model with ideas of FPCA and nonparametric smoothing, the parameter in linear errors-in variables also given briefly in this chapter. Then we discuss how to deal with the scalar response functional linear model with measurement error in two methods which knows as FPCA and nonparametric smoothing. Similar to linear case introduced in the last chapter, due to bring in a known co-variance operator of the measurement error process, the estimator of functional parameter can be gotten. The convergence rate of this estimator also can be found in this chapter. After that, we study the scalar response partial functional linear model with measurement error, for which partial functional linear model is a practical significance extension of functional linear model. Besides, we calculate the estimation of the parameter vector and its asymptotic distribution un-der this situation, then prove the asymptotic property with the mentality of partial linear model with errors-in-variables in the linear part. Finally, simulations show us the estimators in this thesis perform well in the closing chapter.