Likelihood ratio tests for goodness-of-fit of a nonlinear regression model |
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Authors: | Ciprian M Crainiceanu |
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Affiliation: | a Department of Biostatistics, Johns Hopkins University, 615 N. Wolfe Street, Baltimore, MD 21205, USA b School of Operational Research and Industrial Engineering, Cornell University, Rhodes Hall, NY 14853, USA |
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Abstract: | We propose likelihood and restricted likelihood ratio tests for goodness-of-fit of nonlinear regression. The first-order Taylor approximation around the MLE of the regression parameters is used to approximate the null hypothesis and the alternative is modeled nonparametrically using penalized splines. The exact finite sample distribution of the test statistics is obtained for the linear model approximation and can be easily simulated. We recommend using the restricted likelihood instead of the likelihood ratio test because restricted maximum-likelihood estimates are not as severely biased as the maximum-likelihood estimates in the penalized splines framework. |
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Keywords: | 62G10 62E15 62P20 |
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