EFFICIENT ESTIMATION OF LINEAR FUNCTIONALS OF A PROBABILITY MEASURE-P WITH KNOWN MARGINAL DISTRIBUTIONS

• 成果类型: Article
• 署名作者: BICKEL, PJ; RITOV, Y; WELLNER, JA
• 署名单位: Hebrew University of Jerusalem; University of Washington; University of Washington Seattle
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1176348251
• 发表日期: 1991
• 页码: 1316-1346
• 关键词: information; regression

摘要

Suppose that P is the distribution of a pair of random variables (X, Y) on a product space X x Y with known marginal distributions P(X) and P(Y). We study efficient estimation of functions theta(h) = integral h dP for fixed h: X x Y --> R under iid sampling of (X, Y) pairs from P and a regularity condition on P. Our proposed estimator is based on partitions of both X and Y and the modified minimum chi-square estimates of Deming and Stephan (1940). The asymptotic behavior of our estimator is governed by the projection on a certain sum subspace of L2(P), or equivalently by a pair of equations which we call the ACE equations.