Generalised 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 modelling 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 generalised 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.

中文翻译：

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参数引导的广义加性模型适用于并购数据


广义非参数加性模型提供了一种灵活的方法，可以通过链接函数评估多个协变量对感兴趣的一般结果的影响。在此建模框架中，假设每个协变量的影响是非参数的和可加的。然而，在实践中，通常有关于回归函数形状的先验信息，可能来自试点研究或探索性分析。在本文中，我们考虑了这种情况并提出了一种估计程序，其中先验信息用作参数指导来拟合加性模型。具体来说，我们首先使用先验信息（参数指南）为每个回归函数设定一个参数族。删除这些参数趋势后，我们使用非参数广义加性模型估计剩余的非参数函数，并通过加回参数趋势来形成最终估计。我们研究了估计的渐近特性，并表明，当选择一个好的指导时，可以显着降低估计的渐近方差，同时保持渐近方差与无指导估计量相同。我们通过模拟研究观察我们的方法的性能，并通过应用于并购的真实数据集来演示我们的方法。