Large deviation for a least squares estimator in a nonlinear regression model

被引：12
作者：
Yang, Wenzhi [1 ]
Hu, Shuhe [1 ]
机构：
[1] Anhui Univ, Sch Math Sci, Hefei 230039, Peoples R China
来源：
STATISTICS & PROBABILITY LETTERS | 2014年 / 91卷
基金：
中国国家自然科学基金;
关键词：
Large deviation; Least squares estimator; Nonlinear regression model; (rho)over-tilde-mixing random variables; AANA random variables; CONSISTENCY; CONVERGENCE;
D O I：
10.1016/j.spl.2014.04.022
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
By using a large deviation theory of the stochastic process and the moment information of errors, some large deviation results for the least squares estimator theta(n) in a nonlinear regression model are obtained when errors satisfy some general conditions. For some p > 1, examples are presented to show that our results can be used in the case for sup(n >= 1) E vertical bar xi(n)vertical bar(P) = infinity and a better bound can be obtained in the case for sup(n >= 1) E vertical bar xi(n)vertical bar(P) < infinity. Our results generalize and improve the corresponding ones. (C) 2014 Elsevier B.V. All rights reserved.
引用
收藏
页码：135 / 144
页数：10
相关论文
共 30 条
  • [1] Asadian N, 2006, JIRSS-J IRAN STAT SO, V5, P69
  • [2] Bunke H., 1980, Mathematische Operationsforschung und Statistik, Series Statistics, V11, P3, DOI 10.1080/02331888008801521
  • [3] Hall P., 1980, Martingale Limit Theory and Its Application
  • [4] STRONG LAWS FOR DEPENDENT HETEROGENEOUS PROCESSES
    HANSEN, BE
    [J]. ECONOMETRIC THEORY, 1991, 7 (02) : 213 - 221
  • [5] HU SH, 1993, STOCH PROC APPL, V47, P345
  • [6] Consistency for the least squares estimator in nonlinear regression model
    Hu, SH
    [J]. STATISTICS & PROBABILITY LETTERS, 2004, 67 (02) : 183 - 192
  • [7] Hu SH, 2002, SCI CHINA SER A, V45, P137
  • [8] Maximal inequalities for some dependent sequences and their applications
    Hu, Shuhe
    Li, Xiaoqin
    Yang, Wenzhi
    Wang, Xuejun
    [J]. JOURNAL OF THE KOREAN STATISTICAL SOCIETY, 2011, 40 (01) : 11 - 19
  • [9] Ibragimov I. A., 1981, STAT ESTIMATION ASYM, V16
  • [10] Ivanov A., 1989, Statistic Analysis of Random Fields
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