This paper develops the asymptotic theory for the estimation of smooth semiparametric generalized estimating equations models with weakly dependent data. The paper proposes new estimation methods based on smoothed two-step versions of the generalised method of moments and generalised empirical likelihood methods. An important aspect of the paper is that it allows the first-step estimation to have an effect on the asymptotic variances of the second-step estimators and explicitly characterises this effect for the empirically relevant case of the so-called generated regressors. The results of the paper are illustrated with a partially linear model that has not been previously considered in the literature. The proofs of the results utilise a new uniform strong law of large numbers and a new central limit theorem for U-statistics with varying kernels that are of independent interest.

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Keywords Alpha-mixing, empirical likelihood, empirical processes, stochastic equicontinuity, uniform law of large numbers
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Journal Journal of Nonparametric Statistics
Bravo, F. (Francesco), Chu, B, & Jacho-Chávez, D.T. (David T.). (2017). Semiparametric estimation of moment condition models with weakly dependent data. Journal of Nonparametric Statistics, 29(1), 108–136. doi:10.1080/10485252.2016.1254781