Hostname: page-component-6766d58669-tq7bh Total loading time: 0 Render date: 2026-05-21T15:58:53.521Z Has data issue: false hasContentIssue false
  • English
  • Français

AN INTEGRATED KERNEL-WEIGHTED SMOOTHED MAXIMUM SCORE ESTIMATOR FOR THE PARTIALLY LINEAR BINARY RESPONSE MODEL

Published online by Cambridge University Press:  29 November 2013

Jerome M. Krief
Jerome M. Krief*
Affiliation:
University of Virginia
*
*Address correspondence to Jerome Krief, University of Virginia, Department of Economics, Charlottesville, VA 22904.
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper considers a binary response model with a partially linear latent equation, where ϕ is an unknown function and β is a finite-dimensional parameter of interest. Using the principle of smoothed maximum score estimation (Horowitz, 1992; Econometrica 60(3), 505–531), a consistent and asymptotically normal (C.A.N.)estimator for β is proposed under the restriction that the median of the error conditional on the covariates is equal to 0. Furthermore, the rate of convergence in probability is close to the parametric rate, if certain functions admit enough derivatives. This method neither restricts the form of heteroskedasticity in the error term nor suffers from the curse of dimensionality whenever ϕ is multivariate. Some Monte Carlo experiments suggest that this estimator performs well compared with conventional estimators.

Information

Type
ARTICLES
Information
Econometric Theory , Volume 30 , Issue 3 , June 2014 , pp. 647 - 675
Copyright
Copyright © Cambridge University Press 2013 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

REFERENCES

Amemiya, T. (1985) Advanced Econometrics. Harvard University Press.Google Scholar
Blundell, R. & Powell, J. (2004) Endogeneity in semiparametric binary response models. Review of Economic Studies 71, 655–679.Google Scholar
Chaudhuri, P. (1991) Nonparametric quantiles regression. Annals of Statistics 19, 760–777.Google Scholar
Chaudhuri, P., Doksum, K., & Samarov, A. (1997) On average derivative quantile regression. Annals of Statistics 25, 715–744.Google Scholar
Chen, X. (2007) Large sample sieve estimation of semi-nonparametric models. Handbook of Econometrics 6, 5549–5632.Google Scholar
Chen, X. & Pouzo, D. (2012) Estimation of nonparametric conditional moment models with possibly nonsmooth generalized residuals. Econometrica 80, 277–280.Google Scholar
Goldfeld, S., Quandt, R., & Trotter, H. (1966) Maximization by quadratic hill-climbing. Econometrica 34(3), 541–551.Google Scholar
Hong, H. & Tamer, E. (2003) Endogenous binary choice model with median restriction. Economics Letters 80, 219–225.Google Scholar
Horowitz, J. (1992) A smoothed maximum score estimator for the binary response model. Econometrica 60(3), 505–531 Google Scholar
Horowitz, J. (1996) Semiparametric estimation of a regression model with an unknown transformation of the dependent variable. Econometrica 64(1), 103–137 CrossRefGoogle Scholar
Kim, J. & Pollard, D. (1990) Cube root asymptotics. Annals of Statistics 18, 191–219.Google Scholar
Kong, E., Linton, O., & Xia, Y. (2010) Uniform Bahadur representation for local polynomial estimates of M-regression and its application to the additive model. Econometric Theory 26, 145–177.Google Scholar
Krief, J. (2011) Kernel Weighted Smoothed Maximum Score Estimation for Applied Work. LSU Department of Economics Working paper series 2011–07.Google Scholar
Lee, S. (2003) Efficient semi parametric estimation of a partially linear quantile regression model. Econometric Theory 19, 1–31.CrossRefGoogle Scholar
Lewbel, A. (2000) Semiparametric qualitative response model estimation with unknown heteroscedasticity or instrument variables. Journal of Econometrics 97, 145–177.Google Scholar
Manski, C. (1985) Semi parametric analysis of discrete response, asymptotic properties of the maximum score estimator. Journal of Econometrics 27, 313–334.CrossRefGoogle Scholar
Muller, H. (1984) Smooth optimum kernel estimators of regression curves, densities and modes. Annals of Statistics 12, 766–774.Google Scholar
Newey, W. (1987) Efficient estimation of limited dependant variable models with endogenous explanatory variables. Journal of Econometrics 36, 230–251.CrossRefGoogle Scholar
Pagan, A. & Ullah, A. (1999) Non Parametric Econometrics. Cambridge University Press.Google Scholar
Pakes, A. & Pollard, D. (1989) Simulation and the asymptotics of optimization estimators. Econometrica 57, 1027–1057.Google Scholar
Pollard, D. (1984) Convergence of Stochastic Processes. Springer Verlag.Google Scholar
Powell, J.L., Stock, J.H., & Stoker, T.M. (1989) Semiparametric estimation of index coefficients. Econometrica 57, 167–182.CrossRefGoogle Scholar
Rivers, D. & Vuong, Q. (1988) Limited information estimation and exogeneity tests for simultaneous probit models. Journal of Econometrics 39, 347–366.CrossRefGoogle Scholar
Rothe, C. (2009) Semiparametric estimation of binary response models with endogenous regressors. Journal of Econometrics 153, 51–64.Google Scholar
Severini, T. & Wong, W. (1991) On maximum likelihood estimation in infinite dimensional parameter spaces. Annals of Statistics 19, 603–632.Google Scholar
Silverman, B.W. (1986) Density estimation. Chapman and Hall.Google Scholar
Smith, R. & Blundell, R. (1986) An exogeneity test for a simultaneous equation tobit model with an application to labor supply. Econometrica 54, 679–685.Google Scholar