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On local power properties of the LR, Wald, score and gradient tests in nonlinear mixed-effects models

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  • Artur Lemonte

Abstract

The local powers of some tests under the presence of a parameter vector, $$\varvec{\omega }$$ ω say, that is orthogonal to the remaining parameters are studied in this paper. We show that some of the coefficients that define the local powers of the tests remain unchanged regardless of whether $$\varvec{\omega }$$ ω is known or needs to be estimated, whereas the others can be written as the sum of two terms, the first of which being the corresponding term obtained as if $$\varvec{\omega }$$ ω were known, and the second, an additional term yielded by the fact that $$\varvec{\omega }$$ ω is unknown. We apply our general result in the class of nonlinear mixed-effects models and compare the local powers of the tests in this class of models. Copyright The Institute of Statistical Mathematics, Tokyo 2015

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  • Artur Lemonte, 2015. "On local power properties of the LR, Wald, score and gradient tests in nonlinear mixed-effects models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 67(5), pages 885-895, October.
    • Handle: RePEc:spr:aistmt:v:67:y:2015:i:5:p:885-895
    DOI: 10.1007/s10463-014-0478-5
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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. Shinto Eguchi, 1991. "A geometric look at nuisance parameter effect of local powers in testing hypothesis," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 43(2), pages 245-260, June.
    3. Artur Lemonte & Silvia Ferrari, 2012. "The local power of the gradient test," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(2), pages 373-381, April.
    4. Rahul Mukerjee, 1993. "An extension of the conditional likelihood ratio test to the general multiparameter case," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 45(4), pages 759-771, December.
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