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On the asymptotic behaviour of the pseudolikelihood ratio test statistic with boundary problems

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  • Yong Chen
  • Kung-Yee Liang

Abstract

This paper considers the asymptotic distribution of the likelihood ratio statistic T for testing a subset of parameter of interest θ, , , based on the pseudolikelihood , where is a consistent estimator of , the nuisance parameter. We show that the asymptotic distribution of T under H 0 is a weighted sum of independent chi-squared variables. Some sufficient conditions are provided for the limiting distribution to be a chi-squared variable. When the true value of the parameter of interest, , or the true value of the nuisance parameter, , lies on the boundary of parameter space, the problem is shown to be asymptotically equivalent to the problem of testing the restricted mean of a multivariate normal distribution based on one observation from a multivariate normal distribution with misspecified covariance matrix, or from a mixture of multivariate normal distributions. A variety of examples are provided for which the limiting distributions of T may be mixtures of chi-squared variables. We conducted simulation studies to examine the performance of the likelihood ratio test statistics in variance component models and teratological experiments. Copyright 2010, Oxford University Press.

Suggested Citation

  • Yong Chen & Kung-Yee Liang, 2010. "On the asymptotic behaviour of the pseudolikelihood ratio test statistic with boundary problems," Biometrika, Biometrika Trust, vol. 97(3), pages 603-620.
    • Handle: RePEc:oup:biomet:v:97:y:2010:i:3:p:603-620
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    File URL: http://hdl.handle.net/10.1093/biomet/asq031
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    Citations

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    Cited by:

    1. Ana-Maria Staicu & Yingxing Li & Ciprian M. Crainiceanu & David Ruppert, 2014. "Likelihood Ratio Tests for Dependent Data with Applications to Longitudinal and Functional Data Analysis," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(4), pages 932-949, December.
    2. 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.
    3. Ding, Yashuang (Dexter), 2023. "A simple joint model for returns, volatility and volatility of volatility," Journal of Econometrics, Elsevier, vol. 232(2), pages 521-543.
    4. Seunghwa Rho & Peter Schmidt, 2015. "Are all firms inefficient?," Journal of Productivity Analysis, Springer, vol. 43(3), pages 327-349, June.
    5. Kumbhakar, Subal C. & Parmeter, Christopher F. & Tsionas, Efthymios G., 2013. "A zero inefficiency stochastic frontier model," Journal of Econometrics, Elsevier, vol. 172(1), pages 66-76.
    6. Taining Wang & Jinjing Tian & Feng Yao, 2021. "Does high debt ratio influence Chinese firms’ performance? A semiparametric stochastic frontier approach with zero inefficiency," Empirical Economics, Springer, vol. 61(2), pages 587-636, August.
    7. Chuan Hong & Georgia Salanti & Sally C. Morton & Richard D. Riley & Haitao Chu & Stephen E. Kimmel & Yong Chen, 2020. "Testing small study effects in multivariate meta‐analysis," Biometrics, The International Biometric Society, vol. 76(4), pages 1240-1250, December.
    8. 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.
    9. Rui Duan & C. Jason Liang & Pamela Shaw & Cheng Yong Tang & Yong Chen, 2020. "Missing at Random or Not: A Semiparametric Testing Approach," Papers 2003.11181, arXiv.org.
    10. Lucy L. Gao & Daniela Witten & Jacob Bien, 2022. "Testing for association in multiview network data," Biometrics, The International Biometric Society, vol. 78(3), pages 1018-1030, September.
    11. Phill Wheat & Alexander D. Stead & William H. Greene, 2019. "Robust stochastic frontier analysis: a Student’s t-half normal model with application to highway maintenance costs in England," Journal of Productivity Analysis, Springer, vol. 51(1), pages 21-38, February.
    12. Chongliang Luo & Md. Nazmul Islam & Natalie E. Sheils & John Buresh & Jenna Reps & Martijn J. Schuemie & Patrick B. Ryan & Mackenzie Edmondson & Rui Duan & Jiayi Tong & Arielle Marks-Anglin & Jiang Bi, 2022. "DLMM as a lossless one-shot algorithm for collaborative multi-site distributed linear mixed models," Nature Communications, Nature, vol. 13(1), pages 1-10, December.
    13. Christian Ritz, 2013. "Penalized likelihood ratio tests for repeated measurement models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(3), pages 534-547, September.

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