MAXIMUM Lq-LIKELIHOOD ESTIMATION

• 成果类型: Article
• 署名作者: Ferrari, Davide; Yang, Yuhong
• 署名单位: Universita di Modena e Reggio Emilia; University of Minnesota System; University of Minnesota Twin Cities
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/09-AOS687
• 发表日期: 2010
• 页码: 753-783
• 关键词: INFORMATION-THEORY; matrix; robust

摘要

In this paper, the maximum L-q-likelihood estimator (MLqE), a new parameter estimator based on nonextensive entropy [Kibernetika 3 (1967) 30-35] is introduced. The properties of the MLqE are studied via asymptotic analysis and computer simulations. The behavior of the MLqE is characterized by the degree of distortion q applied to the assumed model. When q is properly chosen for small and moderate sample sizes, the MLqE can successfully trade bias for precision, resulting in a substantial reduction of the mean squared error. When the sample size is large and q tends to 1, a necessary and sufficient condition to ensure a proper asymptotic normality and efficiency of MLqE is established.