本文選題：Laplace分布 + 一元線性測量誤差模型　； 參考：《山西師范大學(xué)》2017年碩士論文

【摘要】：Laplace分布是統(tǒng)計(jì)學(xué)中很重要的一類分布.本文基于Laplace分布,分別研究了兩類統(tǒng)計(jì)模型的參數(shù)估計(jì)問題.具體內(nèi)容如下:1.當(dāng)測量誤差服從Laplace分布時(shí),本文基于Laplace分布的Tweedie型公式和回歸校正方法給出了一元線性測量誤差模型參數(shù)的一種新的估計(jì)方法,并在一定的正則條件下,證明了所給估計(jì)的大樣本性質(zhì),包括相合性和漸近正態(tài)性.模擬研究表明在有限樣本下,本文所提出估計(jì)是有效的,且在大多數(shù)情況下優(yōu)于已有的一些估計(jì).2.Laplace分布可以表示成正態(tài)分布和一個(gè)與指數(shù)分布相關(guān)分布的組合,且與最小一乘估計(jì)有緊密的聯(lián)系.基于最小一乘估計(jì)的穩(wěn)健性,本文假定隨機(jī)誤差服從Laplace分布,給出了響應(yīng)變量右刪失的混合線性回歸模型參數(shù)的穩(wěn)健估計(jì).模擬研究和實(shí)例表明,本文所提出的估計(jì)比MLE和EM具有更好的穩(wěn)健性.
[Abstract]:Laplace distribution is an important kind of distribution in statistics. In this paper, we study the parameter estimation of two statistical models based on Laplace distribution. The details are as follows: 1. In this paper, a new method for estimating the parameters of a linear measurement error model is presented based on the Tweedie type formula of Laplace distribution and the regression correction method when the measurement error is obtained from the Laplace distribution, and under certain regular conditions, a new method for estimating the parameters of the linear measurement error model is presented in this paper. It is proved that the large sample properties of the given estimates include consistency and asymptotic normality. Simulation results show that the proposed estimators are valid in finite samples, and in most cases are superior to some existing estimation.2. Laplace distribution can be expressed as a combination of normal distribution and a distribution related to exponential distribution. And it is closely related to the least one multiplication estimate. Based on the robustness of the least one multiplication estimator, this paper assumes that the random error is distributed from the Laplace distribution, and gives the robust estimation of the parameters of the mixed linear regression model with the right censored response variable. Simulation results and examples show that the proposed estimation is more robust than MLE and EM.
【學(xué)位授予單位】：山西師范大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O212.1

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本文編號：2045027