基于长记忆函数型数据条件分布特征量的非参数估计-应用数学专业论文.docxVIP

基于长记忆函数型数据条件分布特征量的非参数估计 基于长记忆函数型数据条件分布特征量的非参数估计 摘 要 函数型数据的理论与应用研究开始于生长曲线分析、分类学、生物力 学、医学等领域，并在最近1 0年发展起来的，特别是最近几年在经济学、 模式识别等领域有广泛的应用．由于相关学科领域中都存在大量的函数型 数据，因此在理论上有新的问题亟待解决．函数型数据的非参数统计推断 特别是回归模型的研究因为其无限维的数据结构与模型给传统的统计推 断理论带来了挑战，需要探究模型中有关未知参数、未知函数算子新的估 计方法及其大样本性质。 本学位论文首先在已有文献的基础上，深入探讨了基于长记忆函数型 条件分布特征量的估计及其相关性质。首先，构造基于函数型数据条件分 布的有关特征量的估计量，包括函数型数据条件中位数的估计，函数型数 据条件众数的估计及函数型数据的条件分位数的估计；然后，利用概率极 限理论的相关知识，研究了估计量的渐近性质。另外，在此研究的基础上， 本文最后提出了进一步拟研究的相关问题。 关键词：长记忆时间序列：函数型数据：条件中位数：条件分位数；条件 众数；依概率收敛 Nonparametric Nonparametric estimation of the conditional distribution characteristic quantity for functional data under long memory conditions Abstract For an introduction and applications of functional data start from several areas including live curves analysis，archeology，neurophysiology， and get up in the recent 1 0 years．Especially，in the reeent 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