一类非线性混合效应模型的估计

发布时间：2018-06-21 01:37

本文选题：B样条 + 高斯—牛顿法　；参考：《南京理工大学》2017年硕士论文

【摘要】：混合效应模型对于相关数据的分析是一个重要的工具,如纵向数据和重复测量数据,而且它还广泛应用于金融、经济等其他方面,最近几年混合效应模型吸引了许多学者的研究兴趣。部分非线性模型是在部分线性模型的基础上发展起来的,我们通过对带有混合效应的部分非线性模型的估计问题进行研究,将这两个模型的优点结合起来,使部分非线性混合效应模型具有更广泛的应用前景。通常,在部分非线性模型中对函数项的研究采用的都是局部(local)的方法,而B样条作为一种整体的估计方法可以弥补局部(local)方法的不足。因此,本文对函数部分的估计将采用B样条的方法来处理。本文考虑了一类非线性混合效应模型的估计问题。这类模型包括部分线性混合效应模型、部分非线性混合效应模型以及纵向数据下的部分非线性混合效应模型。我们主要利用广义最小二乘法和B样条的方法估计联系函数,然后利用该估计量和高斯一牛顿法构造了参数的估计,最后我们还考虑了方差分量的估计问题,并且给出了这些估计量的相合性和渐近正态性。我们通过大量的数字模拟和实例验证了所提方法的有效性,结果表明我们的方法得到的估计效果良好。
[Abstract]:The mixed effect model is an important tool for the analysis of related data, such as longitudinal data and repeated measurement data, and it is also widely used in financial, economic and other aspects. In recent years, the mixed effect model has attracted the interest of many scholars. The partial nonlinear model is developed on the basis of partial linear model. We study the estimation problem of partial nonlinear model with mixed effect and combine the advantages of the two models. The partial nonlinear mixed effect model has a wider application prospect. In general, the method of local localness is used in the study of function term in partial nonlinear model, and the B-spline as a global estimation method can make up for the deficiency of the local localmethod. Therefore, the estimation of the function part in this paper will be treated by B-spline method. In this paper, we consider the estimation of a class of nonlinear mixed effect models. This kind of model includes partial linear mixed effect model, partial nonlinear mixed effect model and partial nonlinear mixed effect model under longitudinal data. We mainly use the generalized least square method and B-spline method to estimate the contact function, then we use the estimator and the Gao Si Newton method to construct the estimation of the parameters. Finally, we consider the estimation of the variance component. The consistency and asymptotic normality of these estimators are given. The effectiveness of the proposed method is verified by a large number of numerical simulations and examples. The results show that the proposed method is effective.
【学位授予单位】：南京理工大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O212.1;F224

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