RANK ESTIMATORS FOR A TRANSFORMATION MODEL
研究了半参数变换模型中Han估计量的根号n一致性和渐近正态性，并引入一类计算更高效的新秩估计量，通过模拟比较了多种估计量的表现。
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 ( n 2 log n ) computations to evaluate the criterion function, compared to O ( n 4 ) 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).