A Simple Formula for Mixing Estimators With Different Convergence Rates

• 成果类型: Article
• 署名作者: Lee, Stephen M. S.; Soleymani, Mehdi
• 署名单位: University of Hong Kong
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2014.960966
• 发表日期: 2015
• 页码: 1463-1478
• 关键词: semiparametric approach; DENSITY-ESTIMATION; regression; derivatives; bootstrap; robust

摘要

Suppose that two estimators, (theta) over cap (S,n) and (theta) over cap (N,n), are available for estimating an unknown parameter theta, and are known to have convergence rates n(1/2) and r(n) = o(n(1/2)), respectively, based on a sample of size n. Typically, the more efficient estimator (theta) over cap (S,n) is less robust than (theta) over cap (N,n), and a definitive choice cannot be easily made between them under practical circumstances. We propose a simple mixture estimator, in the form of a linear combination of (theta) over cap (S,n) and (theta) over cap (N,n), which successfully reaps the benefits of both estimators. We prove that the mixture estimator possesses a kind of oracle property so that it captures the fast n(1/2) convergence rate of (theta) over cap (S,n) when conditions are favorable, and is at least r(n)-consistent otherwise. Applications of the mixture estimator are illustrated with examples drawn from different problem settings including orthogonal function regression, local polynomial regression, density derivative estimation, and bootstrap inferences for possibly dependent data.