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Abstract:
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Semiparametric models have the benefits of being more robust than parametric models yet also more efficient than nonparametric models. In this paper, a semiparametric mixture regression model is proposed and studied. For model identifiability, each error subdistribution is assumed to be symmetric, unimodal and same up to a shift. The semiparametric maximum likelihood estimator is shown to be strongly consistent, its parametric component to be asymptotically efficient and its nonparametric component to have, pointwise and after being multiplied by the cube root of the sample size, a weak limit of a Chernoff random variable times a constant. Simulation studies support the proposed estimation method.
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