Least Absolute Relative Error Estimation
Chen, Kani1; Guo, Shaojun3; Lin, Yuanyuan1; Ying, Zhiliang2
AbstractMultiplicative 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.
KeywordLogarithm transformation Multiplicative regression model Random weighting
Funding ProjectHong Kong RGC[600706] ; Hong Kong RGC[600307] ; Key Laboratory of RCSDS, CAS[2008DP173182] ; National Science Foundation (NSF) ; National Institutes of Health (NIH)
WOS Research AreaMathematics
WOS SubjectStatistics & Probability
WOS IDWOS:000283695300025
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Document Type期刊论文
Corresponding AuthorLin, Yuanyuan
Affiliation1.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
Recommended Citation
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.
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