【作者】 王星惠；

【导师】 朱春华；

【作者基本信息】 安徽大学 ， 概率论与数理统计， 2011， 硕士

【摘要】 近些年来,φ混合序列和ψ混合序列及NOD序列等相依序列的理论研究得到了充分的发展,特别是一些重要的不等式,如Bernstein不等式,Rosenthal型不等式等,这促使了这些序列在统计领域得到了很好的发展.在误差序列为上述相依序列下,本文主要致力于研究半参数和非参数回归模型估计的相合性问题.本文的第二章研究了半参数回归模型Y(j)(xin,tin)=tinβ+g(xin)+e(j)(xin),1≤j≤m,1≤i≤n,综合了最小二乘法和权函数的估计方法,定义了β和g的估计量βm,n和gm,n(x)通过截尾的方法,利用φ混合序列和ψ混合序列的矩不等式以及凸函数的性质,在φ混合和ψ混合误差及其他条件下证明了它们的r(r>2)阶矩相合性和强相合性,推广了胡舒合(1997)的相应结果.本文的第三章考虑了非参数回归模型Yi=g(xi)+εi,1≤i≤n,定义了未知函数g(x)的估计量gn(x),在通常假设的条件下,证明了在误差为NOD序列下g(x)估计量的r(r>1)阶矩相合性,强相合性及完全收敛性.同时,在一致情形的假设下得到了g(x)估计量的一致的矩相合性和强相合性.由于独立序列和NA序列是特殊的NOD序列,我们所得结果推广了非参数回归模型在误差为独立和NA情形下的相应的结果.更多还原

【Abstract】 In recent years.the theory of dependent sequences such asφmixing sequence.Ψmix-ing sequence and NOD sequence and so on, has been sufficiently developed. Especially sev-eral important inequalities are obtained, for instance, Bernstein inequality, Rosenthal’type inequality, and so forth, which greatly improves the development of the applications in statistical fields. In this paper, the consistency of the estimators for semiparametric and nonparametric regressional models are estabilished under the dependent errors above.In Chapter 2, the semiparametric regression model Y(j)(xin,tin)=tinβ+g(xin)+ e(j)(xin),1≤j≤m,1≤i≤n is considered. Based on the methods of least squares and weight function, the estimatorsβm,n and gm,n(x) forβand g are defined, respectively. By using the truncating method, the moment inequalities forφmixing sequence andΨmixing sequence and the properties of the convex functions, we obtain the r-th moment consistency and the strong consistency for these estimators under some mild conditions, which generalize the correponding results of Hu(1997).In Chapter 3, the nonparametric regression model Yi=g(xi)+εi for i=1,2,…,n is discussed.The estimator gn(x) of the unknown function g(x) is defined. For NOD error sequence, under some mild conditions, we investigate the r-th moment consistency, the strong consistency and almostly complete convergence for the estimator. Moreover, under some uniform assumptions,the uniform moment consistency and the uniform strong con-sistency are also obtained. Since independent random variables and negatively associated random variables are the cases of NOD random variables, the results of independent and negatively associated sequences are generalized by the ones that we obtain.更多还原