Least Absolute Relative Error Estimation

• 成果类型: Article
• 署名作者: Chen, Kani; Guo, Shaojun; Lin, Yuanyuan; Ying, Zhiliang
• 署名单位: Hong Kong University of Science & Technology; Columbia University; Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1198/jasa.2010.tm09307
• 发表日期: 2010
• 页码: 1104-1112
• 关键词: regression-estimators; prediction; deviation

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.