Several Nonparametric Structural Models For Spatially Correlated Data

Based on the fact that everything is correlated and not independent with each other,spatial correlation is a classic assumption of econometric models.A challenge issue is constructing appropriate models to accounting for the various kind of data with spatial correlation:· Most works about spatial models adopted a single spatial weights matrix under the parametric framework to describe the spatial effects among individuals,which is contrary to the fact that the spatial correlation is complex and diverse for cross sectional data in practice.· Compared with cross-section data,panel data is a type of repeated observations of many individual or experimental units at different times,and have a wider range of applications,like economics,finance,and society and many other subject areas.There are abundant researches of parametric model or nonparametric model for panel data.To the best of our knowledge,few works have been done for panel data with spatial effect,especially in cases that the number of individuals and the length of time are large.· A correctly specified spatial weights matrix is a crucial assumption in spatial model.Most of the spatial models are based on the fact that the spatial corre-lation is given and lack of theoretical guidance to construct a “correct” spatial weights matrix,which may face the risk of model misspecification in practice.To solve these problems,we propose several new models with the spatial effects and nonparametric additive functions,and establish the theory of statistical inference,based on the theory of spatial model and non-parametric regression model.In detail,this dissertation is divided into six chapters.The first chapter mainly introduces the research background and significance,literature review,research content and the writing framework.The second chapter mainly introduces some basic concepts and research methods used in later chapters,including the construction of the spatial weights matrix and the estimation methods for nonparametric functions.In Chapter 3,we propose nonparametric additive model with high order spatial autoregressive dependence for cross-section data,where the high order correlations are not only for response but also for error term.The estimation procedure is derived into three steps,which combining spline-backfitting method with generalized moment conditions that relieve correlations within the dependent variables.Consistency and asymptotic normality are demonstrated under mild conditions.Specifically,compared with the estimators of nonparametric functions which ignores the cross sectional dependence in errors,the resultant estimators considering the error term is asymptotically more efficient and achieve the well known oracle properties.Simulation studies investing the finite sample performance of the estimation procedure confirm the validity of our asymptotic theory.Besides,an application to Boston housing data serves as a practical illustration.In Chapter 4,we proposes a time varying coefficients spatial dynamic panel data model with unobserved fixed effect and nonparametric additive terms,which allows locally stationary regressors with cross-section size n and time series length T both being large.With the strengths of B-spline and local linear methods,we propose B-spline instrument(B-spline Ⅳ)estimators and two-stage estimators in two steps based on the first-difference model.It is shown that the estimators in the first step are consistent,and the asymptotic normality is also presented for the estimators in the second step.Further,we propose a specification test for the constancy of slopes,and show that our test is asymptotically normally distributed under the null hypothesis.The finite-sample performances of our methods are investigated via Monte Carlo experiments,and the results further confirm the validity of asymptotic theories.Two empirical examples is considered.In Chapter 5,this work addresses two research areas: spatial statistics and functional data analysis.Advances in information technology,we conduct further investigations of functional objects in panel data and propose multiple functional predictors for panel data with cross sectional,where the spatial weights matrix is unknown.Combined Ⅳ moment method and SCAD penalty,a unified framework for selection and estimation of multiple functional predictors and spatial weight matrix is constructed.To improve the performance of multiple functional predictors,we give a post-SCAD estimators.Therefore,not only can we explore the estimation of multiple functional linear regression for panel data,but also recover the network of connections between cross-sectional units.Under mild conditions,we establish the corresponding consistency and oracle properties of the proposed method.Also,some simulation studies are used to evaluate the performance of the proposed method.In Chapter 6,we make a summarisation of the dissertation,and provide the prospects for further work.