A GEOMETRIC COMBINATION ESTIMATOR FOR D-DIMENSIONAL ORDINAL SPARSE CONTINGENCY-TABLES

• 成果类型: Article
• 署名作者: DONG, JP; SIMONOFF, JS
• 署名单位: New York University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1176324702
• 发表日期: 1995
• 页码: 1143-1159
• 关键词: kernel density-estimation

摘要

A geometric combination estimator is proposed for d-dimensional ordinal contingency tables. The proposed estimator is nonnegative. It is shown that, assuming sufficient smoothness and boundary conditions for the underlying probabilities, the rate of convergence of mean summed squared error (MSSE) of this estimator is O(K-1N-8/((d+8))) for d-dimensional tables (d less than or equal to 4) with K cells and sample size N. This rate is optimal under the smoothness assumptions, and is faster than that attained by nonnegative kernel estimates. Boundary kernels for multidimensional tables are also developed for the proposed estimator to relax restrictive boundary conditions, resulting in summed squared error (SSE) being of order O-p(K-1N-8/((d+8))) for all d greater than or equal to 1. The behavior of the new estimator is investigated through simulations and applications to real data. It is shown that even for relatively small tables, these estimators are superior to nonnegative kernel estimators, in sharp contrast to the relatively unimpressive performance of such estimators for continuous data.