Nonparametric sieve estimation of generalized additive model

Associate Professor, Shanghai University of Finance and Economics.

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This paper proposes a nonparametric approach to identify and estimate (with sieves) the generalized additive model with arbitrary grouping and discrete variable(s) when the link function is unknown. Our approach allowing arbitrary grouping provides the foundation to design a data-driven inference procedure which finds the best grouping specification among all possible groupings, and allowing discrete variables is mainly motivated by concerns from applied research. We effectively transform the generalized additive model with unknown link function into a problem which is much easier to estimate by sieve approach. Our estimator for link function is shown to converge at a rate of one covariate, and estimators for component functions within the link can attain nonparametric rates of their own covariates. By simulation, we show that such a method has good performance in finite samples.