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Inference of nonlinear mixed models for clustered data under moment conditions

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  • Zaixing Li

    (China University of Mining and Technology (Beijing)
    State Key Laboratory of Coal Resource and Safe Mining (CUMT))

Abstract

Two statistical inference problems in nonlinear mixed models (NLMM) are considered under only moment conditions on random effects and random errors. First, higher-order moment estimates of random effects and random errors in NLMM are proposed and they turn out to be strongly consistent. Second, a difference-type test $$T_{mDs}$$ T m D s is developed to test whether some sub-vector of random effects exists or not, which is easy to implement without requiring the Monte Carlo method. Its theoretical properties including the power properties are obtained. Moreover, in the special case of testing the existence of random effects, two kinds of tests are also constructed: the global difference-type test $$T_{mDG}$$ T m D G , which is a special case of $$T_{mDs}$$ T m D s , and the modified score-type test $$ST_{n0}$$ S T n 0 , which is motivated by $$ST_{nru}$$ S T n r u in Russo et al. (TEST 21:519–545, 2012). The simulation study indicates that $$T_{mDs}$$ T m D s is the most powerful. A real data analysis is also conducted to investigate the applicability of the procedures.

Suggested Citation

  • Zaixing Li, 2017. "Inference of nonlinear mixed models for clustered data under moment conditions," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(4), pages 759-781, December.
    • Handle: RePEc:spr:testjl:v:26:y:2017:i:4:d:10.1007_s11749-017-0532-8
    DOI: 10.1007/s11749-017-0532-8
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    References listed on IDEAS

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    1. Juvêncio Nobre & Julio Singer & Pranab Sen, 2013. "U-tests for variance components in linear mixed models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(4), pages 580-605, November.
    2. Zaixing Li & Fei Chen & Lixing Zhu, 2014. "Variance Components Testing in ANOVA-Type Mixed Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(2), pages 482-496, June.
    3. Cibele Russo & Reiko Aoki & Gilberto Paula, 2012. "Assessment of variance components in nonlinear mixed-effects elliptical models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(3), pages 519-545, September.
    4. Zaixing Li & Lixing Zhu, 2010. "On Variance Components in Semiparametric Mixed Models for Longitudinal Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 37(3), pages 442-457, September.
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