BOOTSTRAP CONFIDENCE-REGIONS FOR FUNCTIONAL-RELATIONSHIPS IN ERRORS-IN-VARIABLES MODELS

• 成果类型: Article
• 署名作者: BOOTH, JG; HALL, P
• 署名单位: Australian National University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1176349397
• 发表日期: 1993
• 页码: 1780-1791
• 关键词: intervals

摘要

We suggest bootstrap methods for constructing confidence bands (and intervals) for an unknown linear functional relationship in an errors-invariables model. It is assumed that the ratio of error variances is known to lie within an interval LAMBDA = [lambda1, lambda2]. A confidence band is constructed for the range of possible linear relationships when lambda is-an-element-of LAMBDA. Meaningful results are obtained even in the extreme case LAMBDA = [0, infinity], which corresponds to no assumption being made about LAMBDA. The bootstrap bands have several interesting features, which include the following: (i) the bands do not shrink to a line as n --> infinity, unless LAMBDA is a singleton (i.e., lambda1 = lambda2); (ii) -percentile-t versions of the bands enjoy only first-order coverage accuracy, not the second-order accuracy normally found in simpler statistical problems.