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Series estimation for single-index models under constraints

机译：约束下单索级模型的系列估计

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In this paper, a semi-parametric single-index model is investigated. The link function is allowed to be unbounded and has unbounded support that answers a pending issue in the literature. Meanwhile, the link function is treated as a point in an infinitely many dimensional function space which enables us to derive the estimates for the index parameter and the link function simultaneously. This approach is different from the profile method commonly used in the literature. The estimator is derived from an optimisation with the constraint of identification condition for the index parameter, which addresses an important problem in the literature of single-index models. In addition, making use of a property of Hermite orthogonal polynomials, an explicit estimator for the index parameter is obtained. Asymptotic properties for the two estimators of the index parameter are established. Their efficiency is discussed in some special cases as well. The finite sample properties of the two estimates are demonstrated through an extensive Monte Carlo study and an empirical example.
机译：在本文中，研究了半导体单索引模型。允许链接功能无限制，并具有无限性的支持，可以在文献中答案。同时，链接功能被视为无限多维函数空间中的一个点，这使我们能够同时导出索引参数和链路函数的估计。这种方法与文献中常用的轮廓方法不同。估算器从具有索引参数的识别条件的约束来源的估算器，该识别条件地解决了单索引模型的文献中的重要问题。此外，利用Hermite正交多项式的属性，获得了用于索引参数的显式估计器。建立了索引参数的两个估算器的渐近性质。它们的效率也在某些特殊情况下讨论。通过广泛的蒙特卡罗研究和经验例，证明了两种估计的有限样本性质。

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