Estimation of a semiparametric transformation model
Estimation of a semiparametric transformation model
复制标题
DOI：
10.1214/009053607000000848
复制
发表时间：
2008-04-01
影响因子：
4.5
通讯作者：
Van Keilegom, Ingrid
中科院分区：
文献类型：
--
作者：
Linton, Oliver;Sperlich, Stefan;Van Keilegom, Ingrid
本文提出了半参数模型中变换参数的相容估计。问题是寻找到具有预定回归结构(如加法或乘法可分性)的模型空间的最优变换。当模型的其余部分被非参数或半参数估计且满足一定的相合性条件时，我们给出了变换的估计结果。我们提出了两种估计变换参数的方法，一种是最大化轮廓似然函数，另一种是最小化与独立的均方距离。首先讨论了这类模型的辨识问题。然后，我们陈述了一类一般非参数估计的渐近结果。最后，我们给出了变换可分模型的非参数估计的一些特例。在多个仿真中研究了小样本的性能。
This paper proposes consistent estimators for transformation parameters in semiparametric models. The problem is to find the optimal transformation into the space of models with a predetermined regression structure like additive or multiplicative separability. We give results for the estimation of the transformation when the rest of the model is estimated non- or semi-parametrically and fulfills some consistency conditions. We propose two methods for the estimation of the transformation parameter maximizing a profile likelihood function or minimizing the mean squared distance from independence. First the problem of identification of such models is discussed. We then state asymptotic results for a general class of nonparametric estimators. Finally, we give some particular examples of nonparametric estimators of transformed separable models. The small sample performance is studied in several simulations.