SiZer Map for inference with additive models

Abstract

Sizer Map is proposed as a graphical tool for assistance in nonparametric additive regression testing problems. Four problems have been analyzed by using SiZer Map: testing for additivity, testing the components significance, testing parametric models for the components and testing for interactions. The simplicity and flexibility of SiZer Map for our purposes are highlighted from the performed empirical study with several real datasets. With these data, we compare the conclusions derived from SiZer analysis with the global results derived from standard tests, previously proposed in the literature.

SiZer Inference for Varying Coefficient Models

“…In this case, the foregoing two questions involve the crucial problem of choosing an optimal bandwidth or an appropriate smoothing level. However, the optimal choice of the smoothing level for estimating purposes may not be appropriate for the hypothesis testing (Azzalini and Bowman, 1993;González-Manteiga et al, 2008). Moreover, when the coefficients possess different degrees of smoothness, it is more difficult to choose a proper smoothing level for the testing purpose because the coefficients with different degrees of smoothness should be estimated at different smoothing levels Zhang (1999, 2000a).…”

“…The applications of SiZer for time series analysis have been investigated by Park et al (2004Park et al ( , 2007Park et al ( , 2009 and Rondonotti et al (2007). The SiZer inference on the additive models has been studied by González-Manteiga et al (2008) and Martínez-Miranda et al (2008). Several scenarios of SiZer have been developed as a diagnostic device in many areas such as bivariate density estimation (Godtliebsen et al, 2002), survival analysis (Marron and de Uña Álvarez, 2004), local likelihood (Li and Marron, 2005), and smoothing splines (Marron and Zhang, 2005).…”

Nonparametric Comparison of Multiple Regression Curves in Scale-Space

“…SiZer has been also applied to time series data (Park, Marron, and Rondonotti 2004;Park et al 2007;Rondonotti, Marron, and Park 2007;Park, Hannig, and Kang 2009a). In addition, SiZer tools have been developed for jump points detection (Kim and Marron 2006), survival analysis (Marron and de U naÁlvarez 2004), generalized linear models (Li and Marron 2005;Ganguli and Wand 2007;Park and Huh 2013), smoothing spline (Marron and Zhang 2005) and additive models (González-Manteiga, Martínez-Miranda, and Raya-Miranda 2008). Additionally, various Bayesian versions of SiZer have also been proposed as an approach to Bayesian multiscale smoothing (Erästö and Holmström 2005;Godtliebsen and Oigard 2005;Oigard, Rue, and Godtliebsen 2006;Erästö and Holmström 2007;Sørbye et al 2009).…”

Metrics for SiZer map comparison

“…() studied bivariate density estimation, Ganguli and Wand () considered bivariate smoothing, Ganguli and Wand () and Gonzalez‐Manteiga et al . () examined generalized additive models, and Holmstrom and Pasanen () and Vaughan et al . () applied the SiZer idea to images.…”