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Likelihood Based Inference in Non‐linear Regression Models Using the p* and R* Approach

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  • A. S. Tocquet

Abstract

We develop second order asymptotic results for likelihood‐based inference in Gaussian non‐linear regression models. We provide an approximation to the conditional density of the maximum likelihood estimator given an approximate ancillary statistic (the affine ancillary). From this approximation, we derive a statistic to test an hypothesis on one component of the parameter. This test statistic is an adjustment of the signed log‐likelihood ratio statistic. The distributional approximations (for the maximum likelihood estimator and for the test statistic) are of second order in large deviation regions.

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  • A. S. Tocquet, 2001. "Likelihood Based Inference in Non‐linear Regression Models Using the p* and R* Approach," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 28(3), pages 429-443, September.
    • Handle: RePEc:bla:scjsta:v:28:y:2001:i:3:p:429-443
    DOI: 10.1111/1467-9469.00246
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