A Study On Robust Estimate For Dependent Functional Data

Over the past decades, the functional data, arising from Growth curve analysis, Taxonomy, Biomechanics, Medicine and etc, has been developing onto a highly new level. However, due to its abundance in related disciplines, the theory of functional data still needs to be explored further to solve the new problems.This dissertation aims at solving two problems as follows. Firstly, we investigate the nonparametric kernel estimators for a regression function when response variable take values in R and explanatory variable is valued in some abstract function space F. By the robust method, we establish the almost complete convergence rate of the estimators for dependent functional data which extend the existing literature related results in i.i.d.case. Secondly, we investigate a kernel estimation of conditional quantile with robust property, and avoid some problems occurring in the double-kernel method when response variable take values in R and explanatory variable is valued in some abstract space F with the associated semi-metric denoted by d(.,.), which is called function random variables. When the observations are dependent, we establish the almost complete convergence rate of the estimators under some conditions. All we have done in this dissertation extend the existing literature related results.