【作者】 吴波；

【导师】 凌能祥；

【作者基本信息】 合肥工业大学 ， 概率论与数理统计， 2016， 硕士

【摘要】 随着大数据时代的来临,我们实际生活中处理的数据越来越多样化,很多科学实验中得到数据的都是函数型数据,这也是近年来学者们探索的热点之一。对于函数型数据的研究与传统的数据研究是有区别的,传统的数据研究局限在有限维情况下,而函数型数据的研究都是在无限维情况下进行的。需要定义新的度量方式,在夏季电力消耗、光谱数据等的研究中,得到数据的都是函数型数据。因此,对函数型数据理论的研究,在现实科学研究中具有重要意义。但是,现实中我们处理的数据往往是不完整的,由于各种各样的原因,数据可能存在缺失现象,我们得到的只是部分数据。在函数型数据研究中,数据缺失的种类主要有三种：左截断删失、缺失、右删失,关于它们的研究也是学者们的热点。左删失(同左截断删失)在日常生活中,如在医学,地震,生物统计,计量经济学中都有所涉及,因此,对左截断删失条件下的函数型数据的研究是有科学价值的。本文探索的是左截断删失条件下遍历性函数型数据的回归函数的性质,通过设定了平稳遍历数据条件,也取得了一些结果,主要内容如下：一、在左截断删失条件下,通过使用Nadarage-Watson核估计得到了左截断删失条件下遍历性函数型数据的回归函数估计的依概率收敛性、渐近正态性性质；二、由渐近正态性质,我们得到了相关的引理以及回归函数的近似(1-α)的置信区间；三、此外文章的最后我们给出了平稳遍历条件下非参数函数型风险率函数偏差的研究。更多还原

【Abstract】 With the approach of big data,the data we processing in our real life is diversified. A lot of data obtained in scientific experiments is function data. This is one of the hot spots in recent years of scholars. There is a difference between the traditional data research and function data research. Traditional data research is confined to the case of finite dimensionality. However,function data of the research is carried on the case of infinite dimensionality. Needing to define a new measure. In electricity consumption data and spectrometric data research,the data we obtained is function data. Research on the theory of function data, is of great significance in the real scientific research.However,in our real life,the data we processing is incomplete. For various reasons, the data may have missing phenomenon. We get only part of the data. There are three kinds of the data missing:left-truncation,missing data,censored data.Left-truncation in our real life, such as in medicine, earthquake, biostatistics, econometrics are concerned, it has important research value. This paper is to explore nonparametric kernel regression estimation with random left-truncation responses for function data in stationary ergodic. And they have achieved some results, the contents are as follows:Firstly,in the left-truncation condition, by using the Nadarage-Watson kernel estimation of regression function by ergodic function under the condition of the left-truncation data to estimate the convergence in probability, asymptotic normality.Secondly, by the asymptotic normality we obtain some lemmas and as applications the approximate (1-α) confidence interval of the regression function is also presented.Thirdly, in addition,at the end of the paper, we present a study about the bias of the nonparametric hazard function in stationary ergodic condition.更多还原