Subsampling inference in cube root asymptotics with an application to Manski's maximum score estimator
Kim and Pollard (1990) showed that a general class of M-estimators converge at rate nl/3 rather than at the standard rate n1/2 • Many times, this situation arises when the objective function is non-smooth. The limiting distribution is the (almost surely unique) random vector that maximizes a certain Gaussian process and is difficult to analyze analytically. In this paper, we propose the use of the subsampling method for inferential purposes. The general method is then applied to Manski' s maximum score estimator and its small sample performance is highlighted via a simulation study.
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- J. Horowitz, 1996. "Bootstrap Critical Values For Tests Based On The Smoothed Maximum Score Estimator," SFB 373 Discussion Papers 1996,44, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
- Manski, Charles F., 1985. "Semiparametric analysis of discrete response : Asymptotic properties of the maximum score estimator," Journal of Econometrics, Elsevier, vol. 27(3), pages 313-333, March.
- 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.
- Horowitz, Joel L, 1992. "A Smoothed Maximum Score Estimator for the Binary Response Model," Econometrica, Econometric Society, vol. 60(3), pages 505-531, May.
- Stoker, Thomas M, 1986. "Consistent Estimation of Scaled Coefficients," Econometrica, Econometric Society, vol. 54(6), pages 1461-1481, November.
- Powell, James L. & Stock, James H. & Stoker, Thomas M., 1986. "Semiparametric estimation of weighted average derivatives," Working papers 1793-86., Massachusetts Institute of Technology (MIT), Sloan School of Management.
- 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.
- Cosslett, Stephen R, 1983. "Distribution-Free Maximum Likelihood Estimator of the Binary Choice Model," Econometrica, Econometric Society, vol. 51(3), pages 765-782, May.
- Joel L. Horowitz, 1996. "Bootstrap Critical Values for Tests Based on the Smoothed Maximum Score Estimator," Econometrics 9603003, EconWPA.
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