【摘要】：本文針對(duì)縱向數(shù)據(jù),研究部分線性單指標(biāo)模型的穩(wěn)健估計(jì)及其變量選擇,研究?jī)?nèi)容主要有以下幾個(gè)方面:第一,在縱向數(shù)據(jù)下,針對(duì)部分線性單指標(biāo)回歸模型,基于穩(wěn)健分位數(shù)回歸方法,對(duì)模型中單指標(biāo)部分和線性部分都做了分位數(shù)處理,采用局部多項(xiàng)式方法估計(jì)連接函數(shù),在一定的條件下,證明了所得的估計(jì)量具有漸近正態(tài)性,給出了估計(jì)算法的實(shí)施步驟。通過(guò)數(shù)值模擬分析,比較了不同點(diǎn)分位數(shù)回歸連接函數(shù)的估計(jì)效果,驗(yàn)證了所提方法的穩(wěn)健性和有效性。實(shí)例分析Boston房?jī)r(jià)數(shù)據(jù),進(jìn)一步說(shuō)明了所提出方法的實(shí)際應(yīng)用價(jià)值。第二,基于LASSO、ALASSO雙重自適應(yīng)懲罰估計(jì)方法,提出穩(wěn)健化的似然函數(shù),針對(duì)縱向數(shù)據(jù),研究單指標(biāo)線性混合效應(yīng)模型下,固定效應(yīng)和隨機(jī)效應(yīng)的聯(lián)合穩(wěn)健變量選擇,采用懲罰樣條逼近方法,對(duì)單指標(biāo)部分未知連接函數(shù)采取懲罰樣條逼近。在一些正則化條件下,證明了懲罰穩(wěn)健估計(jì)的Oracle性質(zhì)。模擬研究中,比較污染與不污染數(shù)據(jù)時(shí)所提方法的影響,結(jié)果表明所提變量選擇方法具有穩(wěn)健性。實(shí)例分析一組CD4數(shù)據(jù),得到的結(jié)果說(shuō)明所提出方法的有效性和實(shí)用性。
[Abstract]:Based on the longitudinal data, the robust estimation and variable selection of partial linear single index model are studied in this paper. The main contents are as follows: first, under the longitudinal data, for partial linear single index regression model, Based on the robust quantile regression method, the quantiles of the single index part and the linear part of the model are processed, and the connection function is estimated by using the local polynomial method. Under certain conditions, the asymptotic normality of the obtained estimator is proved. The implementation steps of the estimation algorithm are given. By numerical simulation, the estimation effect of the regression connection function of different quantiles is compared, and the robustness and validity of the proposed method are verified. An example is given to illustrate the practical application value of the proposed method by analyzing the Boston housing price data. Secondly, based on the LASSO,ALASSO double adaptive penalty estimation method, a robust likelihood function is proposed. For the longitudinal data, the joint robust variable selection of fixed and random effects is studied under the single parameter linear mixed effect model. The penalty spline approximation method is applied to the partial unknown connection function of a single parameter. Under some regularization conditions, the Oracle property of the penalized robust estimate is proved. In the simulation study, the effects of the proposed method on the pollution and non-pollution data are compared. The results show that the proposed method is robust. An example is given to analyze a set of CD4 data, and the results show the effectiveness and practicability of the proposed method.
【學(xué)位授予單位】：蘭州理工大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類(lèi)號(hào)】：O212.1

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