Discussion: Linear Smoothers and Additive Models

Sparse Partially Linear Additive Models

The generalized partially linear additive model (GPLAM) is a flexible and interpretable approach to building predictive models. It combines features in an additive manner, allowing them to have either a linear or nonlinear effect on the response. However, the assignment of features to the linear and nonlinear groups is typically assumed known. Thus, to make a GPLAM a viable approach in situatio...

Computations for Linear and Generalized Additive Models

Variable Bandwidth and Local Linear Regression Smoothers

In this paper we introduce an appealing nonparametric method for estimating the mean regression function. The proposed method combines the ideas of local linear smoothers and variable bandwidth. Hence, it also inherits the advantages of both approaches. We give expressions for the conditional MSE and MISE of the estimator. Minimization of the MISE leads to an explicit formula for an optimal cho...

Multigrid Smoothers for Ultra-parallel Computing: Additional Theory and Discussion

This paper investigates the properties of smoothers in the context of algebraic multigrid (AMG) running on parallel computers with potentially millions of processors. The development of multigrid smoothers in this case is challenging, because some of the best relaxation schemes, such as the Gauss-Seidel (GS) algorithm, are inherently sequential. Based on the sharp two-grid multigrid theory from...

Power of permutation tests using generalized additive models with bivariate smoothers.

In spatial epidemiology, when applying Generalized Additive Models (GAMs) with a bivariate locally weighted regression smooth over longitude and latitude, a natural hypothesis is whether location is associated with an outcome. An approximate chi-square test (ACST) is available but has an inflated type I error rate. Permutation tests provide alternatives. This research evaluated powers of ACST a...