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)
More accurate confidence intervals in exponential families. (English) Zbl 0752.62027
Summary: Fisher’s theory of maximum likelihood estimation routinely provides approximate confidence intervals for a parameter of interest $\theta$, the standard intervals $\hat\theta\pm z\sb \alpha\hat\sigma$, where $\hat\theta$ is the maximum likelihood estimator, $\hat\sigma$ is an estimate of standard error based on differentiation of the log likelihood function, and $z\sb \alpha$ is a normal percentile point. Recent work has produced systems of better approximate confidence intervals, which look more like exact intervals when exact intervals exist, and in general have coverage probabilities an order of magnitude more accurate than the standard intervals. This paper develops an efficient and dependable algorithm for calculating highly accurate approximate intervals on a routine basis, for parameters $\theta$ defined in the framework of a multiparameter exponential family. The better intervals require only a few times as much computational effort as the standard intervals. A variety of numerical and theoretical arguments are used to show that the algorithm works well, and that the improvement over the standard intervals can be striking in realistic situations.

62F25Parametric tolerance and confidence regions
62G15Nonparametric tolerance and confidence regions
65C99Probabilistic methods, simulation and stochastic differential equations (numerical analysis)
Full Text: DOI