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Robust Inference in Conditionally Linear Nonlinear Regression Models

Abstract.  We consider robust methods of likelihood and frequentist inference for the nonlinear parameter, say α, in conditionally linear nonlinear regression models. We derive closed‐form expressions for robust conditional, marginal, profile and modified profile likelihood functions for α under elliptically contoured data distributions. Next, we develop robust exact‐F confidence intervals for α and consider robust Fieller intervals for ratios of regression parameters in linear models. Several well‐known examples are considered and Monte Carlo simulation results are presented.