Least Absolute Relative Error Estimation

doi:10.1198/jasa.2010.tm09307

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	Least Absolute Relative Error Estimation
	Chen, Kani 1; Guo, Shaojun 3; Lin, Yuanyuan 1; Ying, Zhiliang 2
	2010-09-01
发表期刊	JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
ISSN	0162-1459
卷号	105 期号:491 页码:1104-1112
摘要	Multiplicative regression model or accelerated failure time model, which becomes linear regression model after logarithmic transformation, is useful in analyzing data with positive responses, such as stock prices or life times, that are particularly common in economic/financial or biomedical studies. Least squares or least absolute deviation are among the most widely used criterions in statistical estimation for linear regression model. However, in many practical applications, especially in treating, for example, stock price data, the size of relative error, rather than that of error itself, is the central concern of the practitioners. This paper offers an alternative to the traditional estimation methods by considering minimizing the least absolute relative errors for multiplicative regression models. We prove consistency and asymptotic normality and provide an inference approach via random weighting. We also specify the error distribution, with which the proposed least absolute relative errors estimation is efficient. Supportive evidence is shown in simulation studies. Application is illustrated in an analysis of stock returns in Hong Kong Stock Exchange.
关键词	Logarithm transformation Multiplicative regression model Random weighting
DOI	10.1198/jasa.2010.tm09307
语种	英语
资助项目	Hong Kong RGC[600706] ; Hong Kong RGC[600307] ; Key Laboratory of RCSDS, CAS[2008DP173182] ; National Science Foundation (NSF) ; National Institutes of Health (NIH)
WOS研究方向	Mathematics
WOS类目	Statistics & Probability
WOS记录号	WOS:000283695300025
出版者	AMER STATISTICAL ASSOC
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/10693
专题	中国科学院数学与系统科学研究院
通讯作者	Lin, Yuanyuan
作者单位	1.HKUST, Dept Math, Kowloon, Hong Kong, Peoples R China 2.Columbia Univ, Dept Stat, New York, NY 10027 USA 3.Chinese Acad Sci, Acad Math & Syst Sci, Inst Appl Math, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Chen, Kani,Guo, Shaojun,Lin, Yuanyuan,et al. Least Absolute Relative Error Estimation[J]. JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION,2010,105(491):1104-1112.
APA	Chen, Kani,Guo, Shaojun,Lin, Yuanyuan,&Ying, Zhiliang.(2010).Least Absolute Relative Error Estimation.JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION,105(491),1104-1112.
MLA	Chen, Kani,et al."Least Absolute Relative Error Estimation".JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION 105.491(2010):1104-1112.