Bayesian like R- and M- estimators of change points

Jaromír Antoch; Marie Husková

Discussiones Mathematicae Probability and Statistics (2000)

  • Volume: 20, Issue: 1, page 115-134
  • ISSN: 1509-9423

Abstract

top
The purpose of this paper is to study Bayesian like R- and M-estimators of change point(s). These estimators have smaller variance than the related argmax type estimators. Confidence intervals for the change point based on the exchangeability arguments are constructed. Finally, theoretical results are illustrated on the real data set.

How to cite

top

Jaromír Antoch, and Marie Husková. "Bayesian like R- and M- estimators of change points." Discussiones Mathematicae Probability and Statistics 20.1 (2000): 115-134. <http://eudml.org/doc/287647>.

@article{JaromírAntoch2000,
abstract = {The purpose of this paper is to study Bayesian like R- and M-estimators of change point(s). These estimators have smaller variance than the related argmax type estimators. Confidence intervals for the change point based on the exchangeability arguments are constructed. Finally, theoretical results are illustrated on the real data set.},
author = {Jaromír Antoch, Marie Husková},
journal = {Discussiones Mathematicae Probability and Statistics},
keywords = {estimators of change point; rank statistics; M- and R-estimators; fixed and local changes; fixed changes; confidence intervals; M-estimators; R-estimators; local changes},
language = {eng},
number = {1},
pages = {115-134},
title = {Bayesian like R- and M- estimators of change points},
url = {http://eudml.org/doc/287647},
volume = {20},
year = {2000},
}

TY - JOUR
AU - Jaromír Antoch
AU - Marie Husková
TI - Bayesian like R- and M- estimators of change points
JO - Discussiones Mathematicae Probability and Statistics
PY - 2000
VL - 20
IS - 1
SP - 115
EP - 134
AB - The purpose of this paper is to study Bayesian like R- and M-estimators of change point(s). These estimators have smaller variance than the related argmax type estimators. Confidence intervals for the change point based on the exchangeability arguments are constructed. Finally, theoretical results are illustrated on the real data set.
LA - eng
KW - estimators of change point; rank statistics; M- and R-estimators; fixed and local changes; fixed changes; confidence intervals; M-estimators; R-estimators; local changes
UR - http://eudml.org/doc/287647
ER -

References

top
  1. [1] J. Antoch and M. Husková, Estimators of changes, Nonparametrics, Asymptotics and Time Series, Ghosh S. ed., M. Dekker, (1998a), 533-578. Zbl1069.62515
  2. [2] J. Antoch and M. Husková, Bayesian like estimators of changes, 1998b, J. Stat. Plan. Infer., submitted. Zbl1069.62515
  3. [3] J. Antoch and J.Á. Vísek, Robust estimation in linear model and its computational aspects, Computational Aspects of Model Choice, Physica Verlag, Heidelberg, Antoch J. ed., (1992), 39-104. 
  4. [4] G.W. Cobb, The problem of the Nile: Conditional solution to a change-point problem, Biometrika 65 (1978), 243-251. Zbl0394.62074
  5. [5] M. Csörgo and L. Horváth, Limit Theorems in Change-Point Analysis, J. Wiley, New York 1997. 
  6. [6] L. Dümbgen, The asymptotic behavior of some nonparametric change-point estimators, Ann. Statist. 19 (1991), 1471-1495. Zbl0776.62032
  7. [7] E. Gombay and M. Husková, Rank based estimators of the change-point, J. Stat. Plan. Infer. 67 (1997), 137-154. Zbl0932.62038
  8. [8] D. Hinkley and E. Schechtman, Conditional bootstrap methods in the mean-shift model, Biometrika 74 (1987), 85-93. Zbl0604.62036
  9. [9] P. J. Huber, Robust Statitics, J. Wiley, New York 1981. 
  10. [10] M. Husková, Limit theorems for rank statistics, Statist. and Probab. Letters 30 (1997a), 45-55. 
  11. [11] M. Husková, Limit theorems for M-processes via rank statistics processes, Advances in Combinatorial Methods with Applications to Probability and Statistics, Balakrishnan N. ed., (1997b), 527-533. 
  12. [12] M. Husková, Multivariate rank statistics processes and change-point analysis, Volume of Saleh, 1997c (to appear). 
  13. [13] I. A. Ibragimov and R. Z. Has'minskii, Statistical Estimation. Asymptotic Theory, Springer Verlag, Heidelberg 1981. 
  14. [14] Y. Ritov, Asymptotic efficient estimation of the change-point with unknown distribution, Ann. Statist. 18 (1990), 1829-1839. Zbl0714.62027

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.