本文選題：自適應(yīng)保跳回歸 + 核光滑方法�。� 參考：《東南大學》2016年博士論文

【摘要】：本文主要研究了幾類變系數(shù)模型的統(tǒng)計推斷及應(yīng)用問題,包括帶有跳不連續(xù)系數(shù)的變系數(shù)模型的估計、時變系數(shù)模型的跳檢測和系數(shù)估計、具有異方差的半變系數(shù)模型的正交估計、半變系數(shù)模型的異方差檢驗和縱向數(shù)據(jù)下半變系數(shù)模型的估計.主要內(nèi)容如下：第一章著重介紹幾類變系數(shù)模型的研究背景、研究意義、研究現(xiàn)狀和存在的問題.另外,大致陳述了本文的主要工作,并闡釋了本文的主要創(chuàng)新點.第二章研究帶有跳不連續(xù)系數(shù)的變系數(shù)模型的估計.基于局部線性光滑和保跳回歸技術(shù),我們提出了自適應(yīng)保跳估計方法來估計系數(shù)函數(shù).所提出的方法不需要知道跳點的位置和個數(shù),也不需要進行任何的假設(shè)檢驗,便可自動地識別系數(shù)中的跳點并估計系數(shù)函數(shù).在一些比較弱的假設(shè)條件下,建立了自適應(yīng)保跳估計量的漸近性質(zhì),并通過數(shù)值模擬評價了它的有限樣本性質(zhì).最后通過一個實例分析驗證了所提出方法的有效性.第三章研究時變系數(shù)模型的跳檢測和系數(shù)估計.在實際應(yīng)用中,潛在的系數(shù)曲線可能有奇異點,包括某些未知的位置上有跳點和某些相關(guān)過程的結(jié)構(gòu)變點.檢測這些奇異點對于了解結(jié)構(gòu)改變是非常重要的.基于局部多項式技術(shù)和函數(shù)二階導數(shù)的零穿越性質(zhì),我們提出一個跳檢測方法來檢測系數(shù)函數(shù)中的跳點.然后,利用檢測到的跳點提出了曲線估計方法.進一步地,我們討論了程序參數(shù)的選擇,并在一些弱的條件下建立了估計量在連續(xù)區(qū)間和跳點鄰域內(nèi)的漸近性質(zhì).最后,通過蒙特卡洛試評價所提出方法的有限樣本表現(xiàn),并通過兩個實例分析說明了該方法的用途.第四章討論了具有異方差的半變系數(shù)模型的正交估計.基于矩陣的正交投影、局部線性估計和加權(quán)最小二乘估計,我們提出了一個容易實施的迭代兩階段正交投影估計方法,來估計模型的參數(shù)系數(shù)、非參數(shù)系數(shù)和方差函數(shù).所得到的參數(shù)估計量和非參數(shù)估計量相互不受影響.在比較弱的假設(shè)條件下,建立了它們的相合性和漸近正態(tài)性.然后,實施仿真模擬評價了這些估計量的有限樣本性質(zhì),并通過實例分析說明了所提出方法的有效性.第五章討論了半變系數(shù)模型的異方差檢測.在回歸模型中檢驗方差異是非常重要的,因為參數(shù)的有效推斷要求把異方差考慮在內(nèi).本章提出兩類異方差檢驗方法：一類是基于正態(tài)誤差殘差構(gòu)造檢驗統(tǒng)計量,另一類是利用檢驗異方差等價于檢驗常數(shù)均值的偽殘差的思想構(gòu)造檢驗統(tǒng)計量.然后,用不同速率對應(yīng)同方差的原假設(shè)和備擇假設(shè)建立了檢驗統(tǒng)計量的漸近正態(tài)性.進一步地,通過數(shù)值模擬評價了所提出檢驗統(tǒng)計量的有限樣本表現(xiàn),并通過實例分析說明該檢驗的有效性.第六章研究了縱向數(shù)據(jù)下半變系數(shù)模型的估計.半?yún)?shù)光滑方法通常被用來建模縱向數(shù)據(jù),我們的興趣是提高參數(shù)系數(shù)的效率.基于矩陣的QR分解、局部線性技術(shù)、擬得分估計和擬最大似然估計,提出了一個兩階段正交估計方法,來估計模型中的參數(shù)系數(shù)、非參數(shù)系數(shù)和協(xié)方差函數(shù).所提出的方法可以單獨實施,并且所得的估計量相互不影響.在一些弱的假設(shè)條件下,給出了估計量的漸近性質(zhì).尤其討論了系數(shù)函數(shù)在邊界處的漸近行為.然后,通過數(shù)值模擬評價了估計量的有限樣本表現(xiàn),最后將提出的方法應(yīng)用于分析AIDS數(shù)據(jù).
[Abstract]:This paper mainly studies the statistical inference and application problems of several variable coefficient models, including the estimation of the variable coefficient model with the jump discontinuous coefficient, the jump detection and coefficient estimation of the time-varying coefficient model, the orthogonal estimation of the semi variable coefficient model with heteroscedasticity, the heteroscedasticity test of the semi variable coefficient model and the semi variable coefficient model under the longitudinal data. The main contents are as follows: the first chapter focuses on the research background of several variable coefficient models, research significance, research status and existing problems. In addition, the main work of this paper is described roughly, and the main innovation of this paper is explained. The second chapter studies the estimation of the variable coefficient model with the noncontinuous coefficient of jumping. We propose an adaptive hopping estimation method to estimate the coefficient function. The proposed method does not need to know the position and number of jumping points, and does not need any hypothesis test. It can automatically identify the jump points in the coefficient and estimate the coefficient function. Under some weak assumptions, the method is established. The asymptotic property of adaptive hopping estimator is given and its finite sample properties are evaluated by numerical simulation. Finally, an example is made to verify the effectiveness of the proposed method. The third chapter studies the jump detection and coefficient estimation of the time-varying coefficient model. In practical applications, the potential coefficient curves may have singularity, including some of them. In the unknown position, there are jumps and structural changes in some related processes. Detecting these singularities is very important for understanding structural changes. Based on the local polynomial technique and the zero crossing property of the two order derivative of the function, we propose a jump detection method to detect the jump points in the coefficient function. Then, the detected jump points are proposed. Further, we discuss the selection of the parameters of the program and establish the asymptotic properties of the estimator in the continuous interval and the neighborhood of the jump point in some weak conditions. Finally, the finite sample performance of the proposed method is evaluated by the Monte Carlo method, and the use of the method is illustrated by two examples. Fourth In this chapter, the orthogonal estimation of a semi variable coefficient model with heteroscedasticity is discussed. Based on the orthogonal projection of the matrix, the local linear estimation and the weighted least square estimation, we propose an easy to implement iterative two phase orthogonal projection method to estimate the parameter coefficient, the nonparametric coefficient and the variance function. The measurement and nonparametric estimators are not affected each other. Under the weaker hypothesis, their consistency and asymptotic normality are established. Then, the finite sample properties of these estimators are evaluated by the simulation simulation, and the effectiveness of the proposed method is illustrated by an example. The fifth chapter discusses the different square of the semi variable coefficient model. Difference detection is very important in the regression model, because the effective inference of the parameters is required to take the heteroscedasticity into consideration. In this chapter, two kinds of heteroscedasticity test methods are proposed: one is based on the normal error residual structure test statistics and the other is to use the idea of testing the pseudo residuals equivalent to the mean of the test constant. Then, the asymptotic normality of the test statistics is established by using the original hypothesis and the optional hypothesis of the same variance at different rates. Further, the finite sample performance of the test statistics is evaluated by numerical simulation, and the validity of the test is illustrated by an example. The sixth chapter studies the longitudinal data. The estimation of semi variable coefficient model. Semi parametric smoothing method is usually used to model the longitudinal data. Our interest is to improve the efficiency of parameter coefficients. Based on the matrix QR decomposition, local linear technology, quasi score estimation and quasi maximum likelihood estimation, a two stage orthogonality estimator is proposed to estimate the parameter coefficient and non parameter in the model. Coefficients and covariance functions. The proposed method can be implemented separately and the estimated quantities are not affected each other. Under some weak assumptions, the asymptotic behavior of the estimators is given. The asymptotic behavior of the coefficient function at the boundary is discussed especially. Then, the finite sample performance of the estimator is evaluated by numerical simulation. Finally, the performance of the estimator is evaluated. The method is applied to the analysis of AIDS data.
【學位授予單位】：東南大學
【學位級別】：博士
【學位授予年份】：2016
【分類號】：O212.1

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