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)
Applied asymptotics. Case studies in small-sample statistics. (English) Zbl 1152.62077
Cambridge Series in Statistical and Probabilistic Mathematics 23. Cambridge: Cambridge University Press (ISBN 978-0-521-84703-2/hbk). viii, 236 p. £ 35.00; $ 65.00 (2007).
In fields such as biology, medical sciences, sociology, and economics, researchers often face the situation where the number of available observations, or the amount of available information, is sufficiently small so that approximations based on the normal distribution may be unreliable. Theoretical works over the last quarter-century have yielded new likelihood-based methods that lead to very accurate approximations in finite samples, but these works have had limited impact on statistical practice. This book illustrates by means of realistic examples and case studies how to use the new theory, and investigates how and when it makes a difference to the resulting inference. The treatment is orientated towards practice and is accompanied by code in the R language that enables the methods to be applied in a range of situations of interest to practitioners. The analysis includes some comparisons of higher order likelihood inference with bootstrap and Bayesian methods. The Contents are the following: 1. Introduction; 2. Uncertainty and approximation; 3. Simple illustrations; 4. Discrete data; 5. Regression with continuous responses; 6. Some case studies; 7. Further topics; 8. Likelihood approximations; 9. Numerical implementation; 10. Problems and further results. In the Appendix A we find: Convergence of sequences; The sample mean; Laplace approximation and chi-square approximations. This monograph is very useful for researchers in medicine and biology, as well as in economics and sociology.

62P10Applications of statistics to biology and medical sciences
62-01Textbooks (statistics)
62P20Applications of statistics to economics
62P25Applications of statistics to social sciences
R; mathStatica
Full Text: DOI