The single index model is one of the most popular semiparametric models in applied quantitative sciences. This paper studies a single index model with unknown jumps (SIMJ) that occur in the link function. An adaptive semiparametric estimation procedure is proposed for estimating the index coefficient and link function. The asymptotic normality of the resulting estimators for both the parametric and nonparametric parts can be established under some mild conditions and without specifying the error distribution. We show that the resulting estimators are robust and efficient for different error distributions. In particular, a modified EM algorithm is developed to implement the adaptive semiparametric estimation in practice. Numerical simulations and real data analysis are conducted to illustrate the finite sample performance of the proposed approach.

中文翻译：

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具有跳跃的单指标模型的自适应半参数估计

单指标模型是应用定量科学中最流行的半参数模型之一。本文研究了链接函数中发生的未知跳跃（SIMJ）的单索引模型。提出了一种自适应半参数估计程序来估计指标系数和链接函数。参数和非参数部分的结果估计量的渐近正态性可以在一些温和的条件下建立，而无需指定误差分布。我们表明，由此产生的估计量对于不同的误差分布是稳健且有效的。特别是，开发了一种改进的 EM 算法来在实践中实现自适应半参数估计。进行了数值模拟和实际数据分析，以说明所提出方法的有限样本性能。