Study On Estimation Of A Heteroscedastic Measurement Error Model For Replicated Data

Due to the incomplete measurement resources, the influence of measurement environment, and the level of understanding of the survey crew, measured value does not keep consistent in the true value, which means measurement error exists. Measurement error exists in all scientific experiments and measurement activities throughout, so measurement error analysis and data processing occupy an important place in the scientific experiment and production practice.In this paper, on the basis of measurement error model and replicated data, we discuss parameter estimation of heteroscedastic measurement error model under different restrictions. We develop the EM algorithm to compute the maximum likelihood estimates for the model respectively. We also conduct statistical simulations and applications for diet health data to verify the effective of the EM estimates and confirm their robust behaviors.The main contents and methods in this Master’s thesis are as follows:Chaper 1:As preliminaries, we mainly introduce the background and status of measurement error models, as well as the notions of heavy-tailed distributions.Chaper 2:In this part, we study the parameter estimations of a heteroscedastic measure-ment error model for replicated data under normal distribution. First of all, we analyse the feasibility and rationality of this model. The second, an EM algorithm is applied to compute the maximum likelihood estimates without equation error. In the end, Monte Carlo simulations are discussed to certify the validity of the model, furthermore, we compare the performances of simple least-squares estimation, regression calibration estimation with our method. Chaper 3:On the basis of previous chaper, we discuss the parameter estimation of a heteroscedastic measurement error model for replicated data with equation error. We provide an iterative algorithm of this estimation, then by the means of simulations and applications, we confirm that our model is efficient. Chaper 4:We discuss the estimation of a heteroscedastic measurement error model for replicated data under heavy-tailed distribution. Normal distribution can not consider the in-fluence of outliers, which restricts the accuracy of parameter estimations. Therefore, the above research model has been generalized to more general elliptical distribution. The specific work includes parameter estimations, comparisons of estimation efficiency, and so on. Chaper 5:In summary, we have thoroughly studied parameter estimates for heteroscedas-tic measurement error model for replicated data both with and without equation error, and heteroscedastic measurement error model for replicated data under heavy-tailed distribution. A series of statistical simulations and real examples show the effectiveness of research methods and the robust behaviors of heavy-tailed models.