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A Minimum Power Divergence Class of CDFs and Estimators for Binary Choice Models

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  • Mittelhammer, Ron C Dr.
  • Judge, George G.

Abstract

The Cressie-Read (CR) family of power divergence measures is used to identify a new class of statistical models and estimators for competing explanations of the data in binary choice models. A large flexible class of cumulative distribution functions and associated probability density functions emerge that subsumes the conventional logit model, and forms the basis for a large set of estimation alternatives to traditional logit and probit methods. Asymptotic properties of estimators are identified, and sampling experiments are used to provide a basis for gauging the finite sample performance of the estimators in this new class of statistical models.

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Paper provided by Department of Agricultural & Resource Economics, UC Berkeley in its series Department of Agricultural & Resource Economics, UC Berkeley, Working Paper Series with number qt7bc2828q.

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Date of creation: 08 Jul 2008
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Handle: RePEc:cdl:agrebk:qt7bc2828q

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Keywords: binary choice models and estimators; conditional moment equations; squared error loss; Cressie-Read statistic; information theoretic methods; minimum power divergence;

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  1. Pedro Gozalo & Oliver Linton, 1994. "Local Nonlinear Least Squares Estimation: Using Parametric Information Nonparametrically," Cowles Foundation Discussion Papers 1075, Cowles Foundation for Research in Economics, Yale University.
  2. Gabler, Siegfried & Laisney, Francois & Lechner, Michael, 1993. "Seminonparametric Estimation of Binary-Choice Models with an Application to Labor-Force Participation," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(1), pages 61-80, January.
  3. Han, Aaron K., 1987. "Non-parametric analysis of a generalized regression model : The maximum rank correlation estimator," Journal of Econometrics, Elsevier, vol. 35(2-3), pages 303-316, July.
  4. Yuan, Ke-Hai & Jennrich, Robert I., 1998. "Asymptotics of Estimating Equations under Natural Conditions," Journal of Multivariate Analysis, Elsevier, vol. 65(2), pages 245-260, May.
  5. Newey, W.K., 1989. "Uniform Convergence In Probability And Stochastic Equicontinuity," Papers 342, Princeton, Department of Economics - Econometric Research Program.
  6. Klein, R.W. & Spady, R.H., 1991. "An Efficient Semiparametric Estimator for Binary Response Models," Papers 70, Bell Communications - Economic Research Group.
  7. Richard Smith, 2005. "Efficient information theoretic inference for conditional moment restrictions," CeMMAP working papers CWP14/05, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  8. Horowitz, Joel L, 1992. "A Smoothed Maximum Score Estimator for the Binary Response Model," Econometrica, Econometric Society, vol. 60(3), pages 505-31, May.
  9. Train,Kenneth E., 2009. "Discrete Choice Methods with Simulation," Cambridge Books, Cambridge University Press, number 9780521766555, April.
  10. Manski, Charles F., 1975. "Maximum score estimation of the stochastic utility model of choice," Journal of Econometrics, Elsevier, vol. 3(3), pages 205-228, August.
  11. McFadden, Daniel L., 1984. "Econometric analysis of qualitative response models," Handbook of Econometrics, in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 2, chapter 24, pages 1395-1457 Elsevier.
  12. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-54, July.
  13. Cosslett, Stephen R, 1983. "Distribution-Free Maximum Likelihood Estimator of the Binary Choice Model," Econometrica, Econometric Society, vol. 51(3), pages 765-82, May.
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