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Abstract:
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We introduce a semiparametric generalized linear models framework for time-series data that does not require specification of a working distribution or variance function for the data. Rather, the conditional response distribution is treated as an infinite-dimensional parameter, which is then estimated simultaneously with the usual finite-dimensional parameters via a maximum empirical likelihood approach. A general consistency result for the resulting estimators is shown. Simulations suggest that both estimation and inferences using the proposed method can perform as well as a correctly-specified parametric model even for moderate sample sizes, but is much more robust than parametric methods under model misspecification. The method is also used to analyse the Polio dataset from Zeger (1988).
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