ON NONNEGATIVE UNBIASED ESTIMATORS

• 成果类型: Article
• 署名作者: Jacob, Pierre E.; Thiery, Alexandre H.
• 署名单位: University of Oxford; National University of Singapore
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/15-AOS1311
• 发表日期: 2015
• 页码: 769-784
• 关键词: exact simulation; distributions

摘要

We study the existence of algorithms generating almost surely nonnegative unbiased estimators. We show that given a nonconstant real-valued function f and a sequence of unbiased estimators of lambda is an element of R, there is no algorithm yielding almost surely nonnegative unbiased estimators of f(lambda) is an element of R+. The study is motivated by pseudo-marginal Monte Carlo algorithms that rely on such nonnegative unbiased estimators. These methods allow exact inference in intractable models, in the sense that integrals with respect to a target distribution can be estimated without any systematic error, even though the associated probability density function cannot be evaluated pointwise. We discuss the consequences of our results on the applicability of pseudo-marginal algorithms and thus on the possibility of exact inference in intractable models. We illustrate our study with particular choices of functions f corresponding to known challenges in statistics, such as exact simulation of diffusions, inference in large datasets and doubly intractable distributions.