【作者】 常素英；

【导师】 陈清平；

【作者基本信息】 武汉科技大学 ， 概率论与数理统计， 2009， 硕士

【摘要】 半参数回归模型是一类重要的统计模型,有着广泛的实际应用背景.该模型综合了参数与非参数的信息,比一般的参数模型或非参数模型有更强的解释能力.在理论上,处理这种模型的方法既融合了两类单一性质回归模型的处理方法又不是它们的简单叠加.考虑半参数回归模型y i = xi’β+g(ti)+eii=1,2,,n (1)其中( xi ,ti)是已知的固定设计点列,β∈Rd为未知参数向量,g (?)为定义于[0,1]上的未知可测函数, ei是随机误差. {e i ,i= 1,,n}的均值为零,方差为σ2的独立同分布的随机误差向量.文献中一般用最小二乘法估计参数分量β,而非参数分量g (?)估计问题的大多采用样条估计、核估计、L. S.估计和M-估计等.本文采用了新的推断方法近邻估计,这种方法为半参数回归模型的研究提供了新的途径,使得参数统计量β和g (?)估计应用起来更方便,更切合实际,并在给定的基本假设条件下证明了统计量β和g (?)的渐进性质及其在实际问题中应用,这就为进行大样本参数假设检验奠定了基础,也为以后研究统计量g (?)的估计的收敛速度提供了参考价值.研究结果表明,参数统计量β和g (?)的估计方法比其他估计方法更简洁,参数g (?)的渐进性质得到了证实.半参数回归模型的研究已成为一个重要的研究方向.将极具优势的近邻权函数应用于具有强解释能力的半参数回归模型,这在实际中有着更为广阔的应用背景.深信随着二者在理论和方法上的不断完善和发展,对经济、通信、生物等各个领域都将起着积极的促进作用.更多还原

【Abstract】 Semi-parametric regression model is an important kind of statistical model which has a wide range of practical applications. This model synthesizes the parametric and non-parametric information and possesses more strong explanatory ability than normal parametric and non-parametric model. Theoretically, the way to deal with this model which integrated the methods of the two kinds of regression models of the single property.Consider the semi-parametric regression model as follows: y i = xi’β+g(ti)+eii=1,2,,n (1)In the above equation, ( xi ,ti)is the known fixed design lattice,β∈Rdis the unknown parameter vector, g (?)is the unknown measurable function which define in the range of [0, 1], ei is the stochastic error. {e i ,i= 1,,n}is the independent identically distributed(i. i. d. ) stochastic error vector which the mean value is zero and the variance isσ2.In the references, the normal method to estimate parametric componentβis least square method, but the methods to estimate non-parametric component g (?)are spline approximation, kernel estimation, L. S. estimation, M-estimation et al. This paper presents a new neighbor estimation of deduction method. This method offers new research way for the semi-parametric regression model. After the new strategy used, to estimate the parametric statisticβand g (?)will be more convenient and practical. We have proven the asymptotic property of the statisticβand g (?)and the practical applications of the method, it will lay the foundation for hypothesis testing of the large sample parameters and provide referential value of the further study of convergence rate of the statistic g (?). The results show that the estimation method of the parametric statisticβand g (?)is more brief and compact than other methods and the asymptotic property of parametric statisticβis also has proven.The research of semi-parametric regression model is an important research direction at present. The model which chooses dominant neighborhood function as weight function will have extensive application background. Coupled with the development of the two factors, they will play an active role in the area of communications, economy, biology et al. .更多还原