【摘要】：縱向數(shù)據(jù)經(jīng)常出現(xiàn)在生物,經(jīng)濟(jì),氣象,工業(yè)等領(lǐng)域,在研究連續(xù)性縱向數(shù)據(jù)時(shí)普通的線性回歸模型顯然不能很好的解釋數(shù)據(jù),人們通常采用帶有隨機(jī)效應(yīng)項(xiàng)的混合效應(yīng)模型來(lái)進(jìn)行數(shù)據(jù)建模.我們往往假設(shè)模型中隨機(jī)誤差項(xiàng)與隨機(jī)效應(yīng)項(xiàng)是服從正態(tài)分布的,在此基礎(chǔ)上使用極大似然估計(jì)(MLE)和限制極大似然估計(jì)(RMLE)等方法可以很方便地研究參數(shù)性質(zhì),并且得到很好的結(jié)論.然而實(shí)際數(shù)據(jù)中很難滿足正態(tài)性假設(shè),如果在構(gòu)建數(shù)據(jù)模型時(shí)不顧正態(tài)性假設(shè)的條件要求而強(qiáng)行建模,往往會(huì)得到錯(cuò)誤的結(jié)論.因此本文主要研究線性混合效應(yīng)模型中隨機(jī)誤差項(xiàng)的正態(tài)性檢驗(yàn)以及固定效應(yīng)的參數(shù)估計(jì)問題.由于隨機(jī)誤差是不可觀測(cè)的,所以在進(jìn)行正態(tài)性檢驗(yàn)之前需要對(duì)隨機(jī)誤差進(jìn)行估計(jì),這就需要估計(jì)隨機(jī)效應(yīng)和固定效應(yīng).本文首先使用QR分解的方法將隨機(jī)效應(yīng)項(xiàng)移除,在此基礎(chǔ)上采用SCAD (Smoothly clipped absoluted deviation)方法對(duì)模型的固定效應(yīng)進(jìn)行變量選擇與估計(jì),理論研究表明SCAD方法得到的估計(jì)量在滿足一定的假設(shè)條件下是√n-相合的.其次本文將BHEP(Baringhaus-Henze-Epps-Pulley)多維正態(tài)性檢驗(yàn)方法進(jìn)行了推廣,針對(duì)隨機(jī)誤差的估計(jì)構(gòu)造檢驗(yàn)正態(tài)分布的檢驗(yàn)統(tǒng)計(jì)量.研究發(fā)現(xiàn)本文根據(jù)BHEP方法構(gòu)造的檢驗(yàn)統(tǒng)計(jì)量在原假設(shè)成立的情況下漸近收斂于一個(gè)零均值的高斯過程,并且通過模擬研究驗(yàn)證本文提出方法的有效性.
[Abstract]:Longitudinal data often appear in the biological, economic, meteorological, industrial and other fields. In the study of continuous longitudinal data, the ordinary linear regression model obviously can not explain the data very well. People usually use mixed effect model with random effect term to model data. We often assume that the random error terms and the random effect terms in the model are normally distributed. On this basis, we can easily study the properties of the parameters by using the methods of maximum likelihood estimation (MLE) and restricted maximum likelihood estimation (RMLE). And come to a good conclusion. However, it is difficult to satisfy the normal hypothesis in the actual data. If the data model is constructed regardless of the conditional requirements of the normality assumption, the wrong conclusion will be obtained. In this paper, we mainly study the normality test of random errors and the parameter estimation of fixed effects in the linear mixed effect model. Because the random error is not observable, it is necessary to estimate the random error before the normality test, which requires the estimation of the random effect and the fixed effect. In this paper, the random effect term is removed by QR decomposition method, and then the fixed effect of the model is selected and estimated by SCAD (Smoothly clipped absoluted deviation) method. Theoretical studies show that the estimators obtained by the SCAD method are square n- consistent under certain assumptions. Secondly, the BHEP (Baringhaus-Henze-Epps-Pulley) multidimensional normality test method is extended to construct test statistics for the estimation of random errors. It is found that the test statistics constructed in this paper according to the BHEP method converge to a Gao Si process with zero mean asymptotically under the original hypothesis, and the effectiveness of the proposed method is verified by simulation studies.
【學(xué)位授予單位】：華東師范大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2015
【分類號(hào)】：O212.1

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