Goodness-of-fit test for nonparametric regression models: Smoothing spline ANOVA models as example

Sebastian J. Teran Hidalgo, Michael C. Wu, Stephanie M. Engel and Michael R. Kosorok

Computational Statistics & Data Analysis, 2018, vol. 122, issue C, 135-155

Abstract: Nonparametric regression models do not require the specification of the functional form between the outcome and the covariates. Despite their popularity, the amount of diagnostic statistics, in comparison to their parametric counterparts, is small. We propose a goodness-of-fit test for nonparametric regression models with linear smoother form. In particular, we apply this testing framework to smoothing spline ANOVA models. The test can consider two sources of lack-of-fit: whether covariates that are not currently in the model need to be included, and whether the current model fits the data well. The proposed method derives estimated residuals from the model. Then, statistical dependence is assessed between the estimated residuals and the covariates using the HSIC. If dependence exists, the model does not capture all the variability in the outcome associated with the covariates, otherwise the model fits the data well. The bootstrap is used to obtain p-values. Application of the method is demonstrated with a neonatal mental development data analysis. We demonstrate correct type I error as well as power performance through simulations.

Keywords: Goodness-of-fit; Interaction testing; Smoothing spline models; Bootstrap; Test of independence (search for similar items in EconPapers)
Date: 2018
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0167947318300057
Full text for ScienceDirect subscribers only.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:csdana:v:122:y:2018:i:c:p:135-155

DOI: 10.1016/j.csda.2018.01.004

Access Statistics for this article

Computational Statistics & Data Analysis is currently edited by S.P. Azen

More articles in Computational Statistics & Data Analysis from Elsevier
Bibliographic data for series maintained by Catherine Liu ().