IDEAS home Printed from https://ideas.repec.org/a/bla/jorssb/v66y2004i1p3-16.html
   My bibliography  Save this article

Hypothesis testing in mixture regression models

Author

Listed:
  • Hong‐Tu Zhu
  • Heping Zhang

Abstract

Summary. We establish asymptotic theory for both the maximum likelihood and the maximum modified likelihood estimators in mixture regression models. Moreover, under specific and reasonable conditions, we show that the optimal convergence rate of n−1/4 for estimating the mixing distribution is achievable for both the maximum likelihood and the maximum modified likelihood estimators. We also derive the asymptotic distributions of two log‐likelihood ratio test statistics for testing homogeneity and we propose a resampling procedure for approximating the p‐value. Simulation studies are conducted to investigate the empirical performance of the two test statistics. Finally, two real data sets are analysed to illustrate the application of our theoretical results.

Suggested Citation

  • Hong‐Tu Zhu & Heping Zhang, 2004. "Hypothesis testing in mixture regression models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(1), pages 3-16, February.
    • Handle: RePEc:bla:jorssb:v:66:y:2004:i:1:p:3-16
    DOI: 10.1046/j.1369-7412.2003.05379.x
    as

    Download full text from publisher

    File URL: https://doi.org/10.1046/j.1369-7412.2003.05379.x
    Download Restriction: no
    File URL: https://libkey.io/10.1046/j.1369-7412.2003.05379.x?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    Citations

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


    Cited by:

    1. Hiroyuki Kasahara & Katsumi Shimotsu, 2012. "Testing the Number of Components in Finite Mixture Models," CIRJE F-Series CIRJE-F-867, CIRJE, Faculty of Economics, University of Tokyo.
    2. Georgiev, Iliyan, 2010. "Model-based asymptotic inference on the effect of infrequent large shocks on cointegrated variables," Journal of Econometrics, Elsevier, vol. 158(1), pages 37-50, September.
    3. Hoshino Tadao & Yanagi Takahide, 2022. "Estimating marginal treatment effects under unobserved group heterogeneity," Journal of Causal Inference, De Gruyter, vol. 10(1), pages 197-216, January.
    4. Yang Ning & Yong Chen, 2015. "A Class of Pseudolikelihood Ratio Tests for Homogeneity in Exponential Tilt Mixture Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(2), pages 504-517, June.
    5. Yuzhu Tian & Manlai Tang & Maozai Tian, 2016. "A class of finite mixture of quantile regressions with its applications," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(7), pages 1240-1252, July.
    6. Stéphane Bonhomme & Koen Jochmans & Jean-Marc Robin, 2016. "Non-parametric estimation of finite mixtures from repeated measurements," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(1), pages 211-229, January.
    7. Wong, Tony S.T. & Lam, Kwok Fai & Zhao, Victoria X., 2018. "Asymptotic null distribution of the modified likelihood ratio test for homogeneity in finite mixture models," Computational Statistics & Data Analysis, Elsevier, vol. 127(C), pages 248-257.
    8. Hiroyuki Kasahara & Katsumi Shimotsu, 2017. "Testing the Order of Multivariate Normal Mixture Models," CIRJE F-Series CIRJE-F-1044, CIRJE, Faculty of Economics, University of Tokyo.
    9. Wichitchan, Supawadee & Yao, Weixin & Yang, Guangren, 2019. "Hypothesis testing for finite mixture models," Computational Statistics & Data Analysis, Elsevier, vol. 132(C), pages 180-189.
    10. Ying Huang & Juhee Cho & Youyi Fong, 2021. "Threshold‐based subgroup testing in logistic regression models in two‐phase sampling designs," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 70(2), pages 291-311, March.
    11. Boente, Graciela & Cao, Ricardo & González Manteiga, Wenceslao & Rodriguez, Daniela, 2013. "Testing in generalized partially linear models: A robust approach," Statistics & Probability Letters, Elsevier, vol. 83(1), pages 203-212.
    12. Sylvia Frühwirth-Schnatter, 2011. "Panel data analysis: a survey on model-based clustering of time series," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 5(4), pages 251-280, December.
    13. Meitz, Mika & Saikkonen, Pentti, 2021. "Testing for observation-dependent regime switching in mixture autoregressive models," Journal of Econometrics, Elsevier, vol. 222(1), pages 601-624.
    14. Alexander D. Stead & Phill Wheat & William H. Greene, 2023. "On hypothesis testing in latent class and finite mixture stochastic frontier models, with application to a contaminated normal-half normal model," Journal of Productivity Analysis, Springer, vol. 60(1), pages 37-48, August.
    15. Juan Shen & Xuming He, 2015. "Inference for Subgroup Analysis With a Structured Logistic-Normal Mixture Model," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(509), pages 303-312, March.
    16. James Jaccard, 2012. "The Reasoned Action Model," The ANNALS of the American Academy of Political and Social Science, , vol. 640(1), pages 58-80, March.
    17. Chuan Hong & Yang Ning & Shuang Wang & Hao Wu & Raymond J. Carroll & Yong Chen, 2017. "PLEMT: A Novel Pseudolikelihood-Based EM Test for Homogeneity in Generalized Exponential Tilt Mixture Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(520), pages 1393-1404, October.
    18. Dannemann, Jörn & Holzmann, Hajo, 2010. "Testing for two components in a switching regression model," Computational Statistics & Data Analysis, Elsevier, vol. 54(6), pages 1592-1604, June.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bla:jorssb:v:66:y:2004:i:1:p:3-16. See general information about how to correct material in RePEc.

    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.

    We have no bibliographic references for this item. You can help adding them by using 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 RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: https://edirc.repec.org/data/rssssea.html .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.