Sieve likelihood ratio inference on general parameter space  

作　　者：SHI Jian SHEN Xiaotong 

机构地区：[1]Academy of Mathematics and Systems Science,Beijing 100080,China School of Statistics,University of Minnesota,Minneapolis,MN 55455,USA

出　　处：《Science China Mathematics》2005年第1期67-78,共12页中国科学：数学（英文版）

基　　金：supported in part by National Science Foundation of the USA(Grant IIS-0328802,Grant DMS-0072635);the National Natural Science Foundation of China(Grant.No.10071090 and 10231030).

摘　　要：In this paper,a theory on sieve likelihood ratio inference on general parameterspaces(including infinite dimensional)is studied.Under fairly general regularity conditions,the sieve log-likelihood ratio statistic is proved to be asymptotically X^2 distributed,whichcan be viewed as a generalization of the well-known Wilks' theorem.As an example,asemiparametric partial linear model is investigated.In this paper,a theory on sieve likelihood ratio inference on general parameter spaces(including infinite dimensional) is studied.Under fairly general regularity conditions,the sieve log-likelihood ratio statistic is proved to be asymptotically x2 distributed,which can be viewed as a generalization of the well-known Wilks' theorem.As an example,a emiparametric partial linear model is investigated.

关 键 词：LIKELIHOOD ratio sieves nonparametric and SEMIPARAMETRIC models wavelets. 

分 类 号：N[自然科学总论]