Penalized High Dimensional Empirical Likelihood For Partially Linear Model

The empirical likelihood method, introduced by Owen(1988,1990),is one of the most important statistical inference methods.It has many advantages for constructing confidence intervals.Except that range preserving and transformation respecting, and Bartlett correctable,the most important is that the empirical likelihood regions are shaped"automatically"by the sample without estimating asymptotic variance.Empirical likelihood has been paid great attention by statisticians and economists and has received widely researches and applications.The paper consists of the following chapters:Chapter 1 is mainly focused on introducing the form of partially linear model, the backgrounds and the definition of empirical likelihood method, the form of kinds of penalty functions, for high dimensionality data ,the empirical likelihood method is still applied, with an emphasis on some achievements on the subjects at home and abroad. In chapter 2,according to the weight function W_nj(t ), j = 1,... ,n,where the partially linear model is transformed to linear model.Give the empirical likelihood function ofThe penalized empirical likelihood for parameter estimation and variable selection for problems with diverging numbers of parameters is proposed.By using an appropriate penalty function,we show that PEL has the oracle property.Our results are demonstrated regression coefficients in partially linear models.That is,with probability tending to one,penalized empirical likelihood identifies the model and estimates the nonzero coefficients as efficiently as if the sparsity of the true model were known in advance.The advantage of penalized empirical likelihood is illustrated in testing hypothesis and constructing confidence sets.In chapter 3 numerical simulations confirm our theoretical findings.The proof of main results is given in chapter 4. Firstly,to prove main conclusion,we establish several lemmas which are of significance on their own right,The estimation techniques on random variables of the order, Lagrange multiplier method, Lindeberg-Feller's central-limit theorem play an important role in deriving our results,which show the important position and role in the statistical inference.