Advanced Search
MyIDEAS: Login to save this article or follow this journal

Maximum likelihood estimation of a change-point in the distribution of independent random variables: General multiparameter case


Author Info

  • Bhattacharya, P.K.
Registered author(s):


    In a sequence ofn independent random variables the pdf changes fromf(x, 0) tof(x, 0 + [delta]vn-1) after the firstn[lambda] variables. The problem is to estimate[lambda] [set membership, variant] (0, 1 ), where 0 and [delta] are unknownd-dim parameters andvn --> [infinity] slower thann1/2. Letn denote the maximum likelihood estimator (mle) of[lambda]. Analyzing the local behavior of the likelihood function near the true parameter values it is shown under regularity conditions that ifnn2(- [lambda]) is bounded in probability asn --> [infinity], then it converges in law to the timeT([delta]j[delta])1/2 at which a two-sided Brownian motion (B.M.) with drift1/2([delta]'J[delta])1/2[short parallel]t[short parallel]on(-[infinity], [infinity]) attains its a.s. unique minimum, whereJ denotes the Fisher-information matrix. This generalizes the result for small change in mean of univariate normal random variables obtained by Bhattacharya and Brockwell (1976,Z. Warsch. Verw. Gebiete37, 51-75) who also derived the distribution ofT[mu] for[mu] > 0. For the general case an alternative estimator is constructed by a three-step procedure which is shown to have the above asymptotic distribution. In the important case of multiparameter exponential families, the construction of this estimator is considerably simplified.

    Download Info

    If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
    File URL:
    Download Restriction: Full text for ScienceDirect subscribers only

    As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.

    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 23 (1987)
    Issue (Month): 2 (December)
    Pages: 183-208

    as in new window
    Handle: RePEc:eee:jmvana:v:23:y:1987:i:2:p:183-208

    Contact details of provider:
    Web page:

    Order Information:

    Related research

    Keywords: change-point maximum likelihood estimator weak convergence Brownian motion;


    No references listed on IDEAS
    You can help add them by filling out this form.


    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as in new window

    Cited by:
    1. Elliott, Graham & Muller, Ulrich K., 2007. "Confidence sets for the date of a single break in linear time series regressions," Journal of Econometrics, Elsevier, Elsevier, vol. 141(2), pages 1196-1218, December.
    2. Chen, Gongmeng & Choi, Yoon K. & Zhou, Yong, 2005. "Nonparametric estimation of structural change points in volatility models for time series," Journal of Econometrics, Elsevier, Elsevier, vol. 126(1), pages 79-114, May.
    3. Jandhyala, Venkata K. & Fotopoulos, Stergios B. & Hawkins, Douglas M., 2002. "Detection and estimation of abrupt changes in the variability of a process," Computational Statistics & Data Analysis, Elsevier, Elsevier, vol. 40(1), pages 1-19, July.
    4. Kim, Tae-Hwan & Leybourne, Stephen & Newbold, Paul, 2002. "Unit root tests with a break in innovation variance," Journal of Econometrics, Elsevier, Elsevier, vol. 109(2), pages 365-387, August.
    5. Alastair R. Hall & Sanggohn Han & Otilia Boldea, 2009. "Inference regarding multiple structural changes in linear models with endogenous regressors," Centre for Growth and Business Cycle Research Discussion Paper Series 125, Economics, The Univeristy of Manchester.
    6. Boldea, O. & Hall, A.R. & Han, S., 2012. "Asymptotic distribution theory for break point estimators in models estimated via 2SLS," Open Access publications from Tilburg University urn:nbn:nl:ui:12-5241457, Tilburg University.
    7. Jin, Hao & Zhang, Jinsuo, 2010. "Subsampling tests for variance changes in the presence of autoregressive parameter shifts," Journal of Multivariate Analysis, Elsevier, Elsevier, vol. 101(10), pages 2255-2265, November.
    8. Hall, Alastair R. & Han, Sanggohn & Boldea, Otilia, 2008. "Inference regarding multiple structural changes in linear models estimated via two stage least squares," MPRA Paper 9251, University Library of Munich, Germany, revised 20 Jun 2008.
    9. Cheng, Tsung-Lin, 2009. "An efficient algorithm for estimating a change-point," Statistics & Probability Letters, Elsevier, Elsevier, vol. 79(5), pages 559-565, March.
    10. Bai, Jushan, 1993. "Least squares estimation of a shift in linear processes," MPRA Paper 32878, University Library of Munich, Germany.
    11. Jushan, Bai, 1995. "Estimation of multiple-regime regressions with least absolutes deviation," MPRA Paper 32916, University Library of Munich, Germany, revised Feb 1998.


    This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.


    Access and download statistics


    When requesting a correction, please mention this item's handle: RePEc:eee:jmvana:v:23:y:1987:i:2:p:183-208. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei).

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If references are entirely missing, you can add them using this form.

    If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.