【摘要】：同刪失數(shù)據(jù)一樣,在實(shí)際工作中經(jīng)常會(huì)遇到一些關(guān)于污染數(shù)據(jù)的統(tǒng)計(jì)分析問(wèn)題.1952年Davis [1]首次提出污染數(shù)據(jù)和污染系數(shù)的概念.所謂的“污染”模型即為觀察值的分布未知或至少部分觀察值的分布未知的模型,并且它是由污染源的干擾所致,而這種污染源有別于模型本身,通過(guò)觀察污染數(shù)據(jù)得到的(這些數(shù)據(jù)假設(shè)分布已知).1996年,鄭祖康等提出了兩類污染數(shù)據(jù)回歸模型,并且在回歸誤差和污染源均服從正態(tài)分布假設(shè)條件下利用最小二乘法給出了模型參數(shù)和污染系數(shù)的估計(jì).1998年,陳明華在去掉正態(tài)假設(shè)條件,利用最小二乘法給出了回歸參數(shù)和污染系數(shù)的估計(jì),并且證明了這些估計(jì)量的強(qiáng)相合性.本文的主要工作分為兩個(gè)方面：首先,本文考慮污染數(shù)據(jù)的線性回歸模型,在回歸誤差和污染源均服從Laplace分布下,給出了回歸參數(shù)的最小一乘估計(jì),并證明它的相合性和漸近正態(tài)性；同時(shí)使用模擬對(duì)估計(jì)方法的小樣本性質(zhì)進(jìn)行了分析.模擬結(jié)果顯示,本文所提方法在小樣本情況下表現(xiàn)良好.其次,結(jié)合最小一乘估計(jì)和經(jīng)驗(yàn)似然的思想得到回歸參數(shù)的置信區(qū)間.
[Abstract]:Like censored data, we often encounter some problems of statistical analysis of pollution data in practice. In 1952, Davis [1] put forward the concept of pollution data and pollution coefficient for the first time. The so-called "pollution" model is a model in which the distribution of observed values is unknown, or at least part of the observed values are unknown, and it is caused by the interference of the source of pollution, which is different from the model itself. In 1996, Zheng Zukang and others put forward two kinds of regression models of pollution data. The model parameters and pollution coefficient are estimated by using the least square method under the assumption of regression error and pollution source from normal distribution. In 1998, Chen Minghua removed the normal assumption condition. The regression parameters and pollution coefficients are estimated by the least square method, and the strong consistency of these estimators is proved. The main work of this paper is divided into two aspects: firstly, considering the linear regression model of pollution data, under the Laplace distribution of regression error and pollution source, the least one multiplication estimate of regression parameters is given. Its consistency and asymptotic normality are proved. At the same time, the small sample properties of the estimation method are analyzed by simulation. The simulation results show that the proposed method performs well in the case of small samples. Secondly, the confidence interval of regression parameters is obtained by combining the least one multiplicative estimator and the idea of empirical likelihood.
【學(xué)位授予單位】：南京師范大學(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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