半函数型部分线性回归模型局部线性估计量的渐近性质

发布时间：2018-04-14 08:49

本文选题：函数型数据 + 半参数模型　；参考：《合肥工业大学》2017年硕士论文

【摘要】：随着时代发展及科学技术进步,研究人员在收集数据的途径得到扩展、能力得到提高,收集到的一些数据具有明显的函数型的特点。例如:食品行业猪肉的光谱数据、电力行业日均负荷数据、多个地区的多个指标的经济数据以及地区气温、降水量等数据。因此,对于函数型数据的研究已经成为国内外数理统计学界的研究的热点之一。本学位论文主要由局部线性回归下研究半函数型部分线性回归模型的渐近性质以及函数型数据在实际生活中的应用组成,主要内容如下:一、基于局部线性的半函数型部分线性回归模型的估计在半函数型部分线性回归模型下,通过局部线性回归的方法对模型中函数型非参数部分进行新的估计,得到参数及非参数部分的估计量,并探究参数部分估计量的渐近正态性、函数型非参数估计量的几乎处处收敛速度。最后给出模拟分析,并与经典的Nadarage-Watson核估计方法进行比较,通过箱型图表现出在局部线性方法要比核估计方法的效果好;对于参数部分我们通过直方图检验估计量的渐近正态性。二、基于函数型非参数方法的气温数据分析预测在函数型非参数模型下,我们通过Nadarage-Watson核估计方法分析安徽省1955年1月至2010年12月月度平均气温数据,建立函数型非参数回归模型,并对2010年气温数据进行实证分析研究。同时,从预测值的均方方差以及预测的气温曲线两方面来对有限维非参数回归模型及函数型非参数模型进行比较,从而得出函数型非参数模型的优越性。
[Abstract]:With the development of the times and the progress of science and technology, the way and the ability of the researchers to collect the data have been expanded, and some of the collected data have obvious functional characteristics.For example: the spectral data of pork in food industry, the daily load data of power industry, the economic data of multiple indexes in many regions, and the data of regional temperature, precipitation and so on.Therefore, the study of functional data has become one of the hotspots in the field of mathematical statistics at home and abroad.This dissertation is mainly composed of the asymptotic properties of semi-functional partial linear regression model under local linear regression and the application of functional data in real life. The main contents are as follows: 1.Based on the estimation of locally linear partial linear regression model in the semi-functional partial linear regression model, a new estimation of the functional nonparametric part of the model is carried out by means of the local linear regression method.The estimators of parametric and nonparametric parts are obtained, and the asymptotic normality of parametric partial estimators and almost everywhere convergence rate of functional nonparametric estimators are discussed.Finally, the simulation analysis is given, and compared with the classical Nadarage-Watson kernel estimation method, the box diagram shows that the local linear method is more effective than the kernel estimation method, and for the parameter part, we test the asymptotic normality of the estimator by histogram.Second, the temperature data analysis and prediction based on the functional nonparametric method. Under the functional nonparametric model, we analyze the monthly mean temperature data of Anhui Province from January 1955 to December 2010 by using the Nadarage-Watson kernel estimation method.A functional non-parametric regression model was established and the temperature data in 2010 were analyzed.At the same time, the finite dimensional nonparametric regression model and the functional nonparametric model are compared from the mean square variance of the predicted values and the predicted temperature curve, and the superiority of the functional nonparametric model is obtained.
【学位授予单位】：合肥工业大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O212.1

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