RANK ESTIMATORS FOR A TRANSFORMATION MODEL

Elena Asparouhova, Robert Golanski, Krzysztof Kasprzyk, Robert P. Sherman and Tihomir Asparouhov

Econometric Theory, 2002, vol. 18, issue 05, pages 1099-1120

Abstract: We establish [square root]n-consistency and asymptotic normality of Han s (1987a, Journal of Econometrics 35, 191 209) estimator of the parameters characterizing the transformation function in a semiparametric transformation model. We verify a Vapnik Cervonenkis (VC) condition for the parameterizations of Box and Cox (1964, Journal of the Royal Statistical Society, Series B 34, 187 200) and Bickel and Doksum (1981, Journal of the American Statistical Association 76, 296 311). The verification establishes the VC property for a class of sets generated by a nonlinear function of the transformation parameters. We also introduce a new class of rank estimators for these parameters. These estimators require only O(n2 logn) computations to evaluate the criterion function, compared to O(n4) computations for Han s estimator. We prove that these estimators are also [square root]n-consistent and asymptotically normal. A simulation study compares two of the new estimators to Han s estimator, the fully parametric estimator of Bickel and Doksum (1981), and the nonlinear two-stage least squares estimator of Amemiya and Powell (1981, Journal of Econometrics 17, 351 381).

Date: 2002
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