复杂数据下半参数可加模型的统计推断

为了更好的分析因变量与解释变量之间蕴涵的复杂关系,半参数建模方法在近二十年来得到了人们的广泛关注，被应用到经济管理、金融计量、生物医学、人文社会科学等多个领域中。半参数可加模型作为一类重要的半参数模型得到了统计学家和计量经济学家的重视，然而由于其复杂性，针对该模型的研究结果还相对较少。本课题主要针对半参数可加模型在几类复杂情形下的统计推断问题进行深入研究，主要内容包括如下几个方面：第一，在线性部分自变量存在共线性时，研究模型的有偏估计及其理论性质；第二，在异方差或序列相关等复杂误差方差结构下，研究模型的估计和检验问题；第三，进一步研究变量含误差时模型的估计与检验。本课题无论在理论上还是在应用上都具有重要的研究意义，且富有挑战性，研究成果将丰富半参数模型的研究内容，同时为实际问题的解决提供科学的统计分析方法。

Over the last two decades, some useful semiparametric models have been proposed to capture the underlying relationships between response variables and their associated covariates, and have been widely applied in economics and mangement, finance and ecnometrics, biomedicine, social science and some other fields. Like parametric models, semiparametric models have various forms. Examples include partially linear models, varying coefficent models, additive models, single-index models and their hybrids. As the generalization of partially linear models and additive models, semiparametric (partially linear)additive model is useful in statistical modelling as a multivariate nonparametric fitting technique and has received much attention in statistics and econometrics. Due to its complexity, the tools available for inferences on semiparametric additive models are limited. This project considers statistical inference for the semiparametric models with complicated data, main in several aspects. (1)Biased estimation for this model in case of multicollinearity. (2)Estimation and testing for the model in presence of heteroskedasticity or serial correlation.(3)Estimation and testing for this model when the covariates in the linear part are measured with error. The project is challenging not only useful in theory but also significant in practice. The results will extend the field of semiparametric models and provides statistical methods for real data analysis.