# zbMATH — the first resource for mathematics

##### Examples
 Geometry Search for the term Geometry in any field. Queries are case-independent. Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact. "Topological group" Phrases (multi-words) should be set in "straight quotation marks". au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted. Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff. "Quasi* map*" py: 1989 The resulting documents have publication year 1989. so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14. "Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic. dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles. py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses). la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

##### Operators
 a & b logic and a | b logic or !ab logic not abc* right wildcard "ab c" phrase (ab c) parentheses
##### Fields
 any anywhere an internal document identifier au author, editor ai internal author identifier ti title la language so source ab review, abstract py publication year rv reviewer cc MSC code ut uncontrolled term dt document type (j: journal article; b: book; a: book article)
On bootstrap iteration for coverage correction in confidence intervals. (English) Zbl 0736.62040
The author focuses on the use of the iterated resampling principle introduced by him and {\it P. Hall} [Biometrika 75, 661-671 (1988; Zbl 0659.62053)] to reduce coverage error in confidence intervals. He proves that in the case of one-sided confidence intervals each iteration of the coverage-correction algorithm reduces coverage error by a factor of order $n\sp{-1/2}$, whereas for two-sided intervals the reduction in error is by a factor of order $n\sp{-1}$. He also provides explicit formulas for dominant remainder terms in expansions of coverage error after bootstrap iteration in both one- and two-sided cases. Some illustrative applications are given.

##### MSC:
 62G15 Nonparametric tolerance and confidence regions 62G09 Nonparametric statistical resampling methods 62F25 Parametric tolerance and confidence regions
Full Text: