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Restricted likelihood ratio lack‐of‐fit tests using mixed spline models

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  • Gerda Claeskens

Abstract

Summary. Penalized regression spline models afford a simple mixed model representation in which variance components control the degree of non‐linearity in the smooth function estimates. This motivates the study of lack‐of‐fit tests based on the restricted maximum likelihood ratio statistic which tests whether variance components are 0 against the alternative of taking on positive values. For this one‐sided testing problem a further complication is that the variance component belongs to the boundary of the parameter space under the null hypothesis. Conditions are obtained on the design of the regression spline models under which asymptotic distribution theory applies, and finite sample approximations to the asymptotic distribution are provided. Test statistics are studied for simple as well as multiple‐regression models.

Suggested Citation

  • Gerda Claeskens, 2004. "Restricted likelihood ratio lack‐of‐fit tests using mixed spline models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(4), pages 909-926, November.
    • Handle: RePEc:bla:jorssb:v:66:y:2004:i:4:p:909-926
    DOI: 10.1111/j.1467-9868.2004.05421.x
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    Cited by:

    1. J. Beirlant & G. Claeskens & C. Croux & H. Degryse & H. Dewachter & G. Dhaene & J. Dhaene & I. Gijbels & M. Goovaerts & M. Hubert & F. Roodhooft & W. Schouten & M. Willekens, 2005. "Managing Uncertainty: Financial, Actuarial and Statistical Modeling," Review of Business and Economic Literature, KU Leuven, Faculty of Economics and Business (FEB), Review of Business and Economic Literature, vol. 0(1), pages 23-48.
    2. Susanne M. Schennach, 2014. "Entropic Latent Variable Integration via Simulation," Econometrica, Econometric Society, vol. 82(1), pages 345-385, January.
    3. J. D. Opsomer & G. Claeskens & M. G. Ranalli & G. Kauermann & F. J. Breidt, 2008. "Non‐parametric small area estimation using penalized spline regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(1), pages 265-286, February.
    4. Rong Chen & Hua Liang & Jing Wang, 2011. "Determination of linear components in additive models," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 23(2), pages 367-383.
    5. María José Lombardía & Stefan Sperlich, 2008. "Semiparametric inference in generalized mixed effects models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(5), pages 913-930, November.
    6. Zaili Fang & Inyoung Kim & Jeesun Jung, 2018. "Semiparametric Kernel-Based Regression for Evaluating Interaction Between Pathway Effect and Covariate," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 23(1), pages 129-152, March.
    7. Arūnas P. Verbyla & Joanne Faveri & John D. Wilkie & Tom Lewis, 2018. "Tensor Cubic Smoothing Splines in Designed Experiments Requiring Residual Modelling," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 23(4), pages 478-508, December.
    8. Antoniadis, Anestis & Sapatinas, Theofanis, 2007. "Estimation and inference in functional mixed-effects models," Computational Statistics & Data Analysis, Elsevier, vol. 51(10), pages 4793-4813, June.
    9. Isabel Molina & Ayoub Saei & M. José Lombardía, 2007. "Small area estimates of labour force participation under a multinomial logit mixed model," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 170(4), pages 975-1000, October.
    10. Gerda Claeskens & Jeffrey Hart, 2009. "Rejoinder on: Goodness-of-fit tests in mixed models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 18(2), pages 265-270, August.
    11. Na Li & Xingzhong Xu & Pei Jin, 2011. "Testing the linearity in partially linear models," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 23(1), pages 99-114.
    12. Sonja Greven & Ciprian Crainiceanu, 2013. "On likelihood ratio testing for penalized splines," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 97(4), pages 387-402, October.
    13. Willa W. Chen & Rohit S. Deo, 2009. "The restricted likelihood ratio test at the boundary in autoregressive series," Journal of Time Series Analysis, Wiley Blackwell, vol. 30(6), pages 618-630, November.

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