zbMATH — the first resource for mathematics

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.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
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 the bootstrap and confidence intervals. (English) Zbl 0611.62047
It is known that the bootstrap can be viewed as an empiric one term Edgeworth inversion. The present paper shows that such an inversion given by bootstrap is smooth and does not require preliminary theoretical calculations of the Edgeworth expansion. As such the expansions obtained via bootstrap are useful in describing coverage probabilities or significance levels of a wide class of ”Studentized” statistics. It is shown that the bootstrap may be iterated to give approximation to any desired degree of accuracy. This result is of theoretical nature and explains the encouraging performance of bootstrap methods. Bootstrap iteration involves simulations of simulations and is extremely labourious to implement. However in another paper [see the following review, Zbl 0611.62048] the author provides useful information about the number of simulations required.
Reviewer: B.K.Kale

62G15Nonparametric tolerance and confidence regions
62E20Asymptotic distribution theory in statistics
62G05Nonparametric estimation
65C99Probabilistic methods, simulation and stochastic differential equations (numerical analysis)
Full Text: DOI