Asymptotic Normality Distribution of Simulated Minimum Hellinger Distance Estimators for Continuous Models

• 作者: Andrew Luong Claire Bilodeau
• 来源期刊: 统计学期刊(英文)
• 学科: 数学
• 关键词: Continuous DISTRIBUTION KERNEL Density ESTIMATE CONTINUITY in PROBABILITY DIFFERENTIABILITY in PROBABILITY Hellinger Distance
• 年，卷（期）: 2018,（5）
• 页码范围: 846-860
• 页数: 15页
• 分类号: O1

摘要

Certain distributions do not have a closed-form density, but it is simple to draw samples from them. For such distributions, simulated minimum Hellinger distance (SMHD) estimation appears to be useful. Since the method is distance-based, it happens to be naturally robust. This paper is a follow-up to a previous paper where the SMHD estimators were only shown to be consistent;this paper establishes their asymptotic normality. For any parametric family of distributions for which all positive integer moments exist, asymptotic properties for the SMHD method indicate that the variance of the SMHD estimators attains the lower bound for simulation-based estimators, which is based on the inverse of the Fisher information matrix, adjusted by a constant that reflects the loss of efficiency due to simulations. All these features suggest that the SMHD method is applicable in many fields such as finance or actuarial science where we often encounter distributions without closed-form density.