title: Least Absolute Relative Error Estimation.
abstract: 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.
authors.affiliation: Department of Mathematics, HKUST, Kowloon, Hong Kong, China (makchen@ust.hk).
authors.forename: Kani
authors.initials: K
authors.lastname: Chen
authors.affiliation: Institute of Applied Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, P.R.China (guoshaoj@amss.ac.cn).
authors.forename: Shaojun
authors.initials: S
authors.lastname: Guo
authors.affiliation: Department of Mathematics, HKUST, Kowloon, Hong Kong, China (linyy@ust.hk).
authors.forename: Yuanyuan
authors.initials: Y
authors.lastname: Lin
authors.affiliation: Department of Statistics, 618 Mathematics, Columbia University, New York NY 10027 (zying@stat.columbia.edu).
authors.forename: Zhiliang
authors.initials: Z
authors.lastname: Ying
keywords: Logarithm transformation; Multiplicative regression model; Random weighting; Relative error