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Fast smoothing parameter separation in multidimensional generalized P-splines: the SAP algorithm

机译：多维广义P样条中的快速平滑参数分离：SAP算法

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摘要

A new computational algorithm for estimating the smoothing parameters of a multidimensional penalized spline generalized linear model with anisotropic penalty is presented. This new proposal is based on the mixed model representation of a multidimensional P-spline, in which the smoothing parameter for each covariate is expressed in terms of variance components. On the basis of penalized quasi-likelihood methods, closed-form expressions for the estimates of the variance components are obtained. This formulation leads to an efficient implementation that considerably reduces the computational burden. The proposed algorithm can be seen as a generalization of the algorithm by Schall (1991)-for variance components estimation-to deal with non-standard structures of the covariance matrix of the random effects. The practical performance of the proposed algorithm is evaluated by means of simulations, and comparisons with alternative methods are made on the basis of the mean square error criterion and the computing time. Finally, we illustrate our proposal with the analysis of two real datasets: a two dimensional example of historical records of monthly precipitation data in USA and a three dimensional one of mortality data from respiratory disease according to the age at death, the year of death and the month of death.
机译：提出了一种新的计算算法，用于估计带有各向异性惩罚的多维惩罚样条广义线性模型的平滑参数。此新建议基于多维P样条的混合模型表示，其中，每个协变量的平滑参数均以方差分量表示。在惩罚拟似然法的基础上，获得了估计方差分量的闭式表达式。这种表述导致有效的实现，该实现大大减少了计算负担。提出的算法可以看作是Schall（1991）对方差分量估计的算法的一般化，用于处理随机效应协方差矩阵的非标准结构。通过仿真评估了该算法的实际性能，并根据均方误差准则和计算时间与其他方法进行了比较。最后，我们通过分析两个真实的数据集来说明我们的建议：一个是美国月降水量数据的历史记录的二维示例，另一个是根据死亡年龄，死亡年份和年龄，来自呼吸系统疾病的死亡率数据的三维图。死亡之月。

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