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SOME PROPERTIES OF PROFILE BOOTSTRAP CONFIDENCE INTERVALS
Author(s) -
Kabaila Paul
Publication year - 1993
Publication title -
australian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 0004-9581
DOI - 10.1111/j.1467-842x.1993.tb01326.x
Subject(s) - confidence interval , cdf based nonparametric confidence interval , coverage probability , credible interval , mathematics , robust confidence intervals , statistics , confidence region , tolerance interval , confidence distribution , scalar (mathematics) , interval (graph theory) , combinatorics , geometry
Summary We consider the problem of finding an equi‐tailed confidence interval, with coverage probability (1‐α), for a scalar parameter θ 0 in the presence of a (possibly infinite dimensional) nuisance parameter ψ 0 . It is supposed that the value taken by θ 0 does not restrict the value that ψ 0 may take and vice‐versa. Given a sensible estimate ψ n of ψ 0 , profile bootstrap confidence interval for θ 0 is defined to be the exact equi‐tailed confidence interval with coverage probability (1‐α) assuming that ψ 0 =ψ n . We compare the properties of the profile bootstrap confidence interval and the ordinary bootstrap confidence interval when they are based on studentised and unstudentised quantities. Under mild regularity conditions the profile bootstrap confidence interval is always a subset of the set of allowable values of θ 0 and is transformation‐respecting when based on either an unstudentised quantity or a studentised quantity satisfying certain restrictions. As a confidence interval for the autoregressive parameter of an AR(1) process, the profile bootstrap confidence interval has important advantages over the ordinary bootstrap confidence interval based on a studentised quantity.