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)
Change point estimation using nonparametric regression. (English) Zbl 0867.62033
Summary: We consider a regression model in which the mean function may have a discontinuity at an unknown point. We propose an estimate of the location of the discontinuity based on one-side nonparametric regression estimates of the mean function. The change point estimate is shown to converge in probability at rate $O(n^{-1})$ and to have the same asymptotic distribution as maximum likelihood estimates considered by other authors under parametric regression models. Confidence regions for the location and size of the change are also discussed.

62G07Density estimation
62G15Nonparametric tolerance and confidence regions
Full Text: DOI
[1] DUMBGEN, L. 1991. The asy mptotic behavior of some nonparametric change-point estimates. Änn. Statist. 19 1471 1495. Z.
[2] FAN, J. and GIJBELS, I. 1992. Variable bandwidth and local linear regression smoothers. Ann. Statist. 20 2008 2036. Z. · Zbl 0765.62040 · doi:10.1214/aos/1176348900
[3] HALL, R. and TITTERINGTON, D. M. 1992. Edge-preserving and peak-preserving smoothing. Technometrics 34 429 440. JSTOR: · doi:10.2307/1268942 · http://links.jstor.org/sici?sici=0040-1706%28199211%2934%3A4%3C429%3AEAPS%3E2.0.CO%3B2-W&origin=euclid
[4] HINKLEY, D. V. 1970. Inference about the change-point in a sequence of random variables. Biometrika 57 1 17. Z. JSTOR: · Zbl 0198.51501 · doi:10.1093/biomet/57.1.1 · http://links.jstor.org/sici?sici=0006-3444%28197004%2957%3A1%3C1%3AIATCIA%3E2.0.CO%3B2-9&origin=euclid
[5] IBRAGIMOV, I. A. and HAS’MINSKII, R. Z. 1981. Statistical Estimation: Asy mptotic Theory. Springer, New York. Z.
[6] KIM, H.-J. and SIEGMUND, D. O. 1989. The likelihood ratio test for a change point in simple linear regression. Biometrika 76 409 423. Z. JSTOR: · Zbl 0676.62027 · doi:10.1093/biomet/76.3.409 · http://links.jstor.org/sici?sici=0006-3444%28198909%2976%3A3%3C409%3ATLRTFA%3E2.0.CO%3B2-5&origin=euclid
[7] MCDONALD, J. A. and OWEN, A. B. 1986. Smoothing with split linear fits. Technometrics 28 195 208. Z. JSTOR: · Zbl 0626.65010 · doi:10.2307/1269075 · http://links.jstor.org/sici?sici=0040-1706%28198608%2928%3A3%3C195%3ASWSLF%3E2.0.CO%3B2-2&origin=euclid
[8] MULLER, H.-G. 1992. Change-points in nonparametric regression analysis. Ann. Statist. 20 737 761. Z. · Zbl 0783.62032 · doi:10.1214/aos/1176348654
[9] RITOV, Y. 1990. Asy mptotic efficient estimation of the change point with unknown distributions. Ann. Statist. 18 1829 1839. Z. · Zbl 0714.62027 · doi:10.1214/aos/1176347881
[10] SIEGMUND, D. O. 1988. Confidence sets in change-point problems. Internat. Statist. Rev. 56 31 48. JSTOR: · Zbl 0684.62028 · doi:10.2307/1403360 · http://links.jstor.org/sici?sici=0306-7734%28198804%2956%3A1%3C31%3ACSICP%3E2.0.CO%3B2-O&origin=euclid
[11] MURRAY HILL, NEW JERSEY 07974-2070 E-MAIL: clive@bell-labs.com