Predicting future responses based on possibly mis-specified working models

• 成果类型: Article
• 署名作者: Cai, Tianxi; Tian, Lu; Solomon, Scott D.; Wei, L. J.
• 署名单位: Harvard University; Northwestern University; Harvard University; Harvard University Medical Affiliates; Brigham & Women's Hospital
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asm078
• 发表日期: 2008
• 页码: 7592
• 关键词: of-fit test; intervals; tests

摘要

Under a general regression setting, we propose an optimal unconditional prediction procedure for future responses. The resulting prediction intervals or regions have a desirable average coverage level over a set of covariate vectors of interest. When the working model is not correctly specified, the traditional conditional prediction method is generally invalid. On the other hand, one can empirically calibrate the above unconditional procedure and also obtain its crossvalidated counterpart. Various large and small sample properties of these unconditional methods are examined analytically and numerically. We find that the K-fold crossvalidated procedure performs exceptionally well even for cases with rather small sample sizes. The new proposals are illustrated with two real examples, one with a continuous response and the other with a binary outcome.