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Nonparametric estimation in economics: Bayesian and frequentist approaches

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Justin L. Tobias, Christopher F. Parmeter, Daniel J. Henderson, Joshua C. C. Chan

Published Online: Aug 14 2017

DOI: 10.1002/wics.1406

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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 This article is categorized under: Statistical and Graphical Methods of Data Analysis > Bayesian Methods and Theory Statistical and Graphical Methods of Data Analysis > Density Estimation Statistical and Graphical Methods of Data Analysis > Nonparametric Methods

Kernel density estimates of log hourly wages by gender—using a Gaussian kernel and bandwidths equal to 1.06σ_xn^−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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References

Scott, DW. Multivariate Density Estimation Theory, Practice, and Visualization. New York, NY: Wiley Series in Probability and Mathematical Statistics; 1992.
Li, Q, Racine, J. Nonparametric estimation of distributions with categorical and continuous data. J Multivar Anal 2003, 86:266–292.
Aitchison, J, Aitken, CGG. Multivariate binary discrimination by the kernel method. Biometrika 1976, 63:413–420.
Wang, M‐C, van Ryzin, J. A class of smooth estimators for discrete distributions. Biometrika 1981, 68:301–309.
Epanechnikov, VA. Nonparametric estimation of a multidimensional probability density. Teoriya Veroyatnostei i ee Primeneniya 1969, 14:156–161.
Härdle, W. Applied Nonparametric Regression. Cambridge: Cambridge University Press; 1992.
Li, Q, Racine, J. Nonparametric Econometrics: Theory and Practice. Princeton, NJ: Princeton University Press; 2007.
Silverman, BW. Density Estimation for Statistics and Data Analysis. London: Chapman and Hall; 1986.
Henderson, DJ, Parmeter, CF. Normal reference bandwidths for the general order, multivariate kernel density derivative estimator. Stat Probab Lett 2015, 82:2198–2205.
Henderson, DJ, Parmeter, CF. Applied Nonparametric Econometrics. New York: Cambridge University Press; 2015.
Ouyang, D, Li, Q, Racine, J. Cross‐validation and the estimation of probability distributions with categorical data. J Nonparametr Stat 2006, 18:69–100.
Deheuvels, P. Estimation non Paramétrique de la Densité par Histogrammes Généralisés. Rev Stat Appl 1977, 25:5–42.
Chu, C‐Y, Henderson, DJ, Parmeter, CF. Plug‐in bandwidth selection for kernel density estimation with discrete data. Econometrics 2015, 3:199–214.
Geweke, J. Interpretation and inference in mixture models: simple MCMC works. Comput Stat Data Anal 2007, 51:3529–3550.
Green, PJ. Reversible jump Markov chain Monte Carlo computation and Bayesian model determination. Biometrika 1995, 82:711–732.
Seutheraman, J. A constructive definition of Dirichlet priors. Stat Sin 1994, 4:639–650.
Escobar, MD, West, M. Bayesian density estimation and inference using mixtures. J Am Stat Assoc 1995, 90:577–588.
Kalli, M, Griffin, JE, Walker, SE. Slice sampling mixture models. Stat Comput 2011, 21:93–105.
Walker, SG. Sampling the Dirichlet mixture model with slices. Commun Stat 2007, 36:45–54.
Ishwaran, H, James, LF. Approximate Dirichlet process computing in finite normal mixtures: smoothing and prior information. J Comput Graph Stat 2002, 11:508–532.
Neal, RM. Markov chain sampling methods for Dirichlet process mixture models. J Comput Graph Stat 2000, 9:249–265.
Song, Y. DPM in applications. Notes provided for a short course at the Melbourne Bayesian Econometrics Workshop, November, 2016.
Racine, JS, Li, Q. Nonparametric estimation of regression functions with both categorical and continuous data. J Econ 2004, 119:99–130.
Fan, J, Gijbels, I. Local Polynomial Modelling and Its Applications. London: Chapman and Hall; 1996.
Henderson, DJ, Li, Q, Parmeter, CF, Yao, S. Gradient‐based smoothing parameter selection for nonparametric regression estimation. J Econom 2016, 184:233–241.
Polachek, SW. Differences in expected post‐school investment and determinant of market wage differentials. Int Econ Rev 1975, 16:451–470.
Koop, G, Poirier, DJ. Bayesian variants of some classical semiparametric regression techniques. J Econom 2004, 123:259–282.
Koop, G, Poirier, DJ, Tobias, JL. Semiparametric Bayesian inference in multiple equations models. J Appl Economet 2004, 19:827–849.

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