Fan Jianqing, Maity Arnab, Wang Yihui, Wu Yichao
Frederick L. Moore '18 Professor of Finance, Department of Operations Research and Financial Engineering, Princeton University, Princeton, NJ 08544, USA.
J Nonparametr Stat. 2013 Jan 1;25(1):109-128. doi: 10.1080/10485252.2012.735233.
Generalized nonparametric additive models present a flexible way to evaluate the effects of several covariates on a general outcome of interest via a link function. In this modeling framework, one assumes that the effect of each of the covariates is nonparametric and additive. However, in practice, often there is prior information available about the shape of the regression functions, possibly from pilot studies or exploratory analysis. In this paper, we consider such situations and propose an estimation procedure where the prior information is used as a parametric guide to fit the additive model. Specifically, we first posit a parametric family for each of the regression functions using the prior information (parametric guides). After removing these parametric trends, we then estimate the remainder of the nonparametric functions using a nonparametric generalized additive model, and form the final estimates by adding back the parametric trend. We investigate the asymptotic properties of the estimates and show that when a good guide is chosen, the asymptotic variance of the estimates can be reduced significantly while keeping the asymptotic variance same as the unguided estimator. We observe the performance of our method via a simulation study and demonstrate our method by applying to a real data set on mergers and acquisitions.
广义非参数加法模型提供了一种灵活的方法，通过链接函数来评估几个协变量对一般感兴趣结果的影响。在这个建模框架中，人们假设每个协变量的影响是非参数且可加的。然而，在实际中，通常可以从初步研究或探索性分析中获得关于回归函数形状的先验信息。在本文中，我们考虑这种情况，并提出一种估计程序，其中先验信息被用作拟合加法模型的参数指南。具体来说，我们首先利用先验信息（参数指南）为每个回归函数设定一个参数族。去除这些参数趋势后，我们然后使用非参数广义加法模型估计非参数函数的其余部分，并通过加回参数趋势形成最终估计。我们研究了估计量的渐近性质，并表明当选择一个好的指南时，估计量的渐近方差可以显著降低，同时保持渐近方差与无指南估计量相同。我们通过模拟研究观察了我们方法的性能，并通过应用于一个关于并购的真实数据集来展示我们的方法。
