ABSTRACT In this paper we propose model-based penalties for smoothing spline density estimation and inference. These model-based penalties incorporate indefinite prior knowledge that the density is close to, but not necessarily in a family of distributions. We will use the Pearson and generalisation of the generalised inverse Gaussian families to illustrate the derivation of penalties and reproducing kernels. We also propose new inference procedures to test the hypothesis that the density belongs to a specific family of distributions. We conduct extensive simulations to show that the model-based penalties can substantially reduce both bias and variance in the decomposition of the Kullback-Leibler distance, and the new inference procedures are more powerful than some existing ones. We further demonstrate the empirical performance of the proposed method with a real world data set.

中文翻译：

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基于模型惩罚的样条密度估计和推理

摘要 在本文中，我们提出了基于模型的惩罚，用于平滑样条密度估计和推理。这些基于模型的惩罚包含了密度接近但不一定在分布族中的不确定先验知识。我们将使用 Pearson 和广义逆高斯族的泛化来说明惩罚和再生核的推导。我们还提出了新的推理程序来检验密度属于特定分布族的假设。我们进行了广泛的模拟，以表明基于模型的惩罚可以大大减少 Kullback-Leibler 距离分解中的偏差和方差，并且新的推理程序比一些现有的推理程序更强大。