【作者】 王燕；

【导师】 王学军；

【作者基本信息】 安徽大学 ， 统计学， 2020， 硕士

【摘要】 数理统计是统计分析的基础,由于实际生产的需要,采用数学分析方法建立的统计模型逐渐成为统计学科研究的焦点之一.非参数统计是统计学的一个重要分支,而绝大多数非参数统计方法主要基于统计量的某种渐近性质,故统计量的渐近性质是解决一些统计模型中相关问题的关键.本文主要研究EV回归模型,半参数回归模型和非线性回归模型中未知参数估计量的渐近理论,其中涉及到最小二乘估计量和GM估计量.可以指出的是:当样本量不大时,GM估计量(一种带有积分的估计量)相比PC估计量具有更高的准确性.我们讨论END随机变量序列加权和的完全f-矩收敛性的问题,此结果改进和推广了已有结果,继而得到END随机误差下,EV回归模型中未知参数最小二乘估计量的完全相合性,并给出数值模拟.我们从模型出发,探究φ,混合误差下,半参数回归模型中未知参数最小二乘估计量的矩相合性,展现较弱矩条件下的相合性结果;同时,我们也给出了数值模拟.然后探究在α混合误差下,非线性回归模型中GM估计量的渐近结果,包括矩相合性和渐近正态性,并根据结果给出符合理论条件的数据模拟.本文的结果完善和丰富了相依或混合随机变量序列的概率极限理论与重要统计模型中统计量的渐近理论,具有重要的实际意义.更多还原

【Abstract】 Mathematical statistics is the basis of statistical analysis.Due to the needs in practical produce,the statistical model established by mathemat-ical analysis method has gradually become one of the focuses of statistical research.Nonparametric statistics is an important branch of statistics and many nonparametric methods are mainly based on some asymptotic proper-ties of statistics.Therefore,the asymptotic properties of statistics are crucial to handle the problems in statistical models.In this paper,we mainly study the asymptotic theories of estimators in EV regression model,semiparametric regression model and nonlinear regres-sion model,which mainly deal with least square estimator and GM estimator.It should be noted that GM estimator(an estimator involved with integral form)has higher accuracy than PC estimator,when the sample size is not large enough.We discuss the problem about complete f-moment convergence for weighted sums of END random variables,which improves and generalizes the corresponding ones in existing achievements.Then we get the complete consistency for least squares estimators of unknown parameters in EV regres-sion model under END random errors,and then give the numerical simulation.From the model itself,we study the moment consistency for least squares es-timator of unknown parameter and function in the semiparametric regression model with φ-mixing errors under the condition of weaker moment condition;at the same time,we give the numerical simulation.We study the asymptotic results for GM estimator in the nonlinear regression model under α-mixing er-rors,including the r-th moment consistency and asymptotic normality.After that,a simulation satisfying the theoretical conditions is given according to theorems.The results of this paper enrich and improve the probability limit the-ory for dependent and mixing random variables and asymptotic theory for estimators in the important statistical models,and have practical significance.更多还原