Semilogarithmic Error Based Estimation and Its Related Distributions

• Activity Number: 279
• Type: Contributed
• Date/Time: Tuesday, August 4, 2009 : 8:30 AM to 10:20 AM
• Sponsor: IMS
• Author(s): Masato Kagihara*+
• Companies: Fukuoka University
• Keywords: Probability distribution ; Heavy right tail ; Positive dependent variable ; Loss function ; Maximum likelihood method ; Regression analysis

Abstract

As a tool for solving positive regression problems, Yoneda (2006, JORSJ) proposed `semi-logarithmic loss function' which has the same form as Jeffreys information and shares the idea with Stein's loss. Under the statistical model such that the minimization of the semi-logarithmic loss is equivalent to the maximization of likelihood function, the derived and its related distributions are novel to the best of the author's knowledge. Therefore, this paper studies their distributional properties and compares them with other distributions. It is shown that the induced multiplicative error distribution does not have even its first moment. Its scale family is shown to belong to exponential family and further generalizations are explored. Based on those results, statistical properties of the semi-logarithmic loss based estimator are studied, and the potential of the method are discussed.