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Bayesian Variants of Some classical Semiparametric Regression Techniques

This paper develops new Bayesian methods for semiparametric inference in the partial linear Normal regression model: y = z*beta + f(x) + epsilon, where f(.) is an unknown function. These methods draw solely on the Normal linear regression model with natural conjugate prior. Hence, analytical finite sample results are available which do not suffer from problems of theoretical and computational complexity which plague the existing literature. Constrained and unconstrained estimation are considered as is testing of parametric regression models against semiparametric alternatives and prediction. We discuss how these methods can, at some cost in terms of computational complexity, be extended to other models (e.g. qualitative choice models or those involving censoring or truncation) and provide precise details for semiparametric probit and tobit models. We show how the assumption of Normal errors can easily be relaxed. Our methods are illustrated using artificial and real data sets.

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Paper provided by Edinburgh School of Economics, University of Edinburgh in its series ESE Discussion Papers with number 73.

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Length: 41
Date of creation: Apr 2001
Date of revision:
Handle: RePEc:edn:esedps:73
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  1. Hardle, W., 1992. "Applied Nonparametric Methods," Papers 9204, Catholique de Louvain - Institut de statistique.
  2. John F. Geweke & Michael P. Keane, 1997. "Mixture of normals probit models," Staff Report 237, Federal Reserve Bank of Minneapolis.
  3. Geweke, John, 1986. "Exact Inference in the Inequality Constrained Normal Linear Regression Model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 1(2), pages 127-41, April.
  4. John Xu Zheng, 1996. "A consistent test of functional form via nonparametric estimation techniques," Journal of Econometrics, Elsevier, vol. 75(2), pages 263-289, December.
  5. Adonis Yatchew, 1998. "Nonparametric Regression Techniques in Economics," Journal of Economic Literature, American Economic Association, vol. 36(2), pages 669-721, June.
  6. Shiller, Robert J, 1973. "A Distributed Lag Estimator Derived from Smoothness Priors," Econometrica, Econometric Society, vol. 41(4), pages 775-88, July.
  7. Matzkin, Rosa L., 1986. "Restrictions of economic theory in nonparametric methods," Handbook of Econometrics, in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 42, pages 2523-2558 Elsevier.
  8. McCulloch, Robert & Rossi, Peter E., 1994. "An exact likelihood analysis of the multinomial probit model," Journal of Econometrics, Elsevier, vol. 64(1-2), pages 207-240.
  9. Poirier, Dale J., 1998. "Revising Beliefs In Nonidentified Models," Econometric Theory, Cambridge University Press, vol. 14(04), pages 483-509, August.
  10. Oliver LINTON, . "Applied nonparametric methods," Statistic und Oekonometrie 9312, Humboldt Universitaet Berlin.
  11. Leamer, Edward E, 1982. "Sets of Posterior Means with Bounded Variance Priors," Econometrica, Econometric Society, vol. 50(3), pages 725-36, May.
  12. Hong, Yongmiao & White, Halbert, 1995. "Consistent Specification Testing via Nonparametric Series Regression," Econometrica, Econometric Society, vol. 63(5), pages 1133-59, September.
  13. Iwata, Shigeru, 1996. "Bounding posterior means by model criticism," Journal of Econometrics, Elsevier, vol. 75(2), pages 239-261, December.
  14. Chib, Siddhartha, 1992. "Bayes inference in the Tobit censored regression model," Journal of Econometrics, Elsevier, vol. 51(1-2), pages 79-99.
  15. Kajal Lahiri, 2005. "Analysis of Panel Data," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 87(4), pages 1093-1095.
  16. Fernandez, Carmen & Osiewalski, Jacek & Steel, Mark F. J., 1997. "On the use of panel data in stochastic frontier models with improper priors," Journal of Econometrics, Elsevier, vol. 79(1), pages 169-193, July.
  17. Dale J. Poirier, 1995. "Intermediate Statistics and Econometrics: A Comparative Approach," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262161494, June.
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