Approximation to the Distribution of the Least Squares Estimators in Two Dimensional Cosine Models by Randomly Weighted Bootstrap  

作　　者：Yuan-yuan ZHAO Rui-xing MING Yao-hua WU 

机构地区：[1]Department of Statistics and Finance,University of Science and Technology of China [2]School of Mathematical Sciences,Nanjing Normal University [3]Institute of Finance and Statistics,Nanjing Normal University [4]School of Statistics and Mathematics,Zhejiang Gongshang University

出　　处：《Acta Mathematicae Applicatae Sinica》2013年第4期765-776,共12页应用数学学报（英文版）

基　　金：Supported by the National Natural Science Foundations of China(No.11271193);Humanities and Social Sciences Planning Foundation of Chinese Ministry of Education(11YJA910004);Natural Science Foundation of the Jiangsu Higher Education Institutions of China(11KJB110005);Key Research Base for Humanities and Social Sciences of Zhejiang Provincial High Education Talents(Statistics of Zhejiang Gongshang University)

摘　　要：Recently, Kundu and Gupta （Metrika, 48：83 C 97, 1998） established the asymptotic normality of the least squares estimators in the two dimensional cosine model. In this paper, we give the approximation to the general least squares estimators by using random weights which is called the Bayesian bootstrap or the random weighting method by Rubin （Annals of Statistics, 9：130 C 134, 1981） and Zheng （Acta Math. Appl. Sinica （in Chinese）, 10（2）： 247 C 253, 1987）. A simulation study shows that this approximation works very well.Recently, Kundu and Gupta （Metrika, 48：83 C 97, 1998） established the asymptotic normality of the least squares estimators in the two dimensional cosine model. In this paper, we give the approximation to the general least squares estimators by using random weights which is called the Bayesian bootstrap or the random weighting method by Rubin （Annals of Statistics, 9：130 C 134, 1981） and Zheng （Acta Math. Appl. Sinica （in Chinese）, 10（2）： 247 C 253, 1987）. A simulation study shows that this approximation works very well.

关 键 词：two dimensional model least squares estimator Bayesian bootstrap random weighting method 

分 类 号：O211.3[理学—概率论与数理统计]