本文選題：函數(shù)型數(shù)據 + 半參數(shù)模型　； 參考：《合肥工業(yè)大學》2017年碩士論文

【摘要】：隨著時代發(fā)展及科學技術進步,研究人員在收集數(shù)據的途徑得到擴展、能力得到提高,收集到的一些數(shù)據具有明顯的函數(shù)型的特點。例如:食品行業(yè)豬肉的光譜數(shù)據、電力行業(yè)日均負荷數(shù)據、多個地區(qū)的多個指標的經濟數(shù)據以及地區(qū)氣溫、降水量等數(shù)據。因此,對于函數(shù)型數(shù)據的研究已經成為國內外數(shù)理統(tǒng)計學界的研究的熱點之一。本學位論文主要由局部線性回歸下研究半函數(shù)型部分線性回歸模型的漸近性質以及函數(shù)型數(shù)據在實際生活中的應用組成,主要內容如下:一、基于局部線性的半函數(shù)型部分線性回歸模型的估計在半函數(shù)型部分線性回歸模型下,通過局部線性回歸的方法對模型中函數(shù)型非參數(shù)部分進行新的估計,得到參數(shù)及非參數(shù)部分的估計量,并探究參數(shù)部分估計量的漸近正態(tài)性、函數(shù)型非參數(shù)估計量的幾乎處處收斂速度。最后給出模擬分析,并與經典的Nadarage-Watson核估計方法進行比較,通過箱型圖表現(xiàn)出在局部線性方法要比核估計方法的效果好;對于參數(shù)部分我們通過直方圖檢驗估計量的漸近正態(tài)性。二、基于函數(shù)型非參數(shù)方法的氣溫數(shù)據分析預測在函數(shù)型非參數(shù)模型下,我們通過Nadarage-Watson核估計方法分析安徽省1955年1月至2010年12月月度平均氣溫數(shù)據,建立函數(shù)型非參數(shù)回歸模型,并對2010年氣溫數(shù)據進行實證分析研究。同時,從預測值的均方方差以及預測的氣溫曲線兩方面來對有限維非參數(shù)回歸模型及函數(shù)型非參數(shù)模型進行比較,從而得出函數(shù)型非參數(shù)模型的優(yōu)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.
【學位授予單位】：合肥工業(yè)大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：O212.1

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