Effective Nonparametric Estimation in the Case of Severely Discretized Data
Almost all economic data sets are discretized or rounded to some extent. This paper proposes a regression and a density estimator that work especially well when the data is very discrete. The estimators are a weighted average of the data, and the weights are composed of cubic B-splines. Unlike most nonparametric settings, where it is assumed that the observed data comes from a continuum of possibilities, we base our work on the assumption that the discreteness becomes finer as the sample size increases. Rates of convergence and asymptotic distributional results are derived under this condition.
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