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Nonparametric estimation in economics: Bayesian and frequentist approaches

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We review Bayesian and classical approaches to nonparametric density and regression estimation and illustrate how these techniques can be used in economic applications. On the Bayesian side, density estimation is illustrated via finite Gaussian mixtures and a Dirichlet Process Mixture Model, while nonparametric regression is handled using priors that impose smoothness. From the frequentist perspective, kernel‐based nonparametric regression techniques are presented for both density and regression problems. Both approaches are illustrated using a wage dataset from the Current Population Survey. WIREs Comput Stat 2017, 9:e1406. doi: 10.1002/wics.1406

Kernel density estimates of log hourly wages by gender—using a Gaussian kernel and bandwidths equal to 1.06σxn−1/5.
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Posterior mean of the regression function relating age to log hourly earnings (left panel); posterior mean of the marginal effect (gradient) of age on earnings (right panel).
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Kernel estimated conditional mean function relating age to log hourly earnings (left panel); kernel estimated marginal effect (gradient) of age on earnings (right panel).
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Density estimates of log hourly wages by gender—finite mixture and Dirichlet process mixture model results.
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Computational Intensive Statistical Methods > Density Estimation and Curve Fitting
Computational Bayesian Methods > Bayesian Methods and Theory
Statistical Methods > Nonparametric Statistics

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