Bootstrap Confidence Regions for Functional Relationships in Errors-in- Variables Models

Booth, James G. ; Hall, Peter

Ann. Statist., Tome 21 (1993) no. 1, p. 1780-1791 / Harvested from Project Euclid

Résumé

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 $\Lambda = \lbrack\lambda_1, \lambda_2\rbrack$. A confidence band is constructed for the range of possible linear relationships when $\lambda \in \Lambda$. Meaningful results are obtained even in the extreme case $\Lambda = \lbrack 0, \infty\rbrack$, 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 $n \rightarrow \infty$, unless $\Lambda$ is a singleton (i.e., $\lambda_1 = \lambda_2)$; (ii) percentile-$t$ versions of the bands enjoy only first-order coverage accuracy, not the second-order accuracy normally found in simpler statistical problems.

Détail

Publié le : 1993-12-14
Classification:  Bootstrap,  confidence band,  confidence interval,  Edgeworth expansion,  errors-in-variables model,  functional relationship,  percentile method,  percentile-$t$ method,  structural relationship,  62J05,  62G15