Nonparametric Estimation Of The Conditional Distribution Characteristic Quantity For Functional Data Under Long Memory Conditions

For an introduction and applications of functional data start from several areas including live curves analysis, archeology, neurophysiology, and get up in the recent 10 years. Especially, in the recent several years, a lot of attention has been paid to criminology and economics. There is an abundant functional data appear in the related academic domain, therefore has many principle problems urgently want to get solution. Non-parameter statistical inference of functional data about regression model research, For infinite data structure and model bring the challenge to traditional statistics, need to study related unknown element and unknown functional data in the model.In this thesis, on the base of bibliography we already have, we are interested in the problem of estimating the conditional distribution characteristic when the explanatory data are of functional type, under long memory dependent structure. We give the convergence in probability of the kernel type estimator constructed from functional data under long memory conditions. We also give the consistency of the estimator with functional data under long memory conditions. Then we give the convergence of the kernel type conditional quantile estimator with functional data under long memory conditions, including conditional mode estimator, conditional median estimator, conditional quantile estimator.At last,there are many other further research problems to solve with this relative field.