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Abstract:
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The validity of inference under a generalized linear model directly depends on correctly specifying either a distribution for the response if maximizing a likelihood, or a functional form for the variance if resorting to quasi-likelihood and related methods. In order to relax such assumptions, the structure of the exponential family can be exploited to construct semi-parametric models. The corresponding probability density function can be seen as an exponential tilt, in the direction of the observation-specific mean, from a common baseline density. The latter can then be estimated along with the parameters in the mean equation, which allows to estimate standard errors asymptotically as well as if the true distribution, or variance function, were known. However, so far only computationally prohibitive methods such as empirical likelihood have been suggested. We propose an alternative semi-parametric formulation which relies on splines for approximating the logarithm of the baseline density and introduce an efficient algorithm which scales well with the sample size. Simulations and a real data example are presented to illustrate the good performances of this alternative method.
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