Regularised rank quasi-likelihood estimation for generalised additive models

Abstract

Generalised additive models (GAMs) provide flexible models for a wide array of data sources. In the past, improvements of GAM estimation have focused on the smoothers used in the local scoring algorithm used for estimation, but poor prediction for non-Gaussian data motivates the need for robust estimation of GAMs. In this paper, rank-based estimation, as a robust and efficient alternative to the likelihood-based estimation of GAMs, is proposed. It is shown that rank GAM estimators can be obtained through iteratively reweighted likelihood-based GAM estimation which we call the iterated regularised rank quasi-likelihood (IRRQL). Simulation experiments support the use of rank-based GAM estimation for heavy-tailed or contaminated sources of data.

Keywords:

• Wilcoxon score function
• iteratively reweighted least squares
• smoothing spline
• robust estimation

MSC2010 codes:

• 62G05
• 62G30
• 62G35
• 62J12

Data availability statement

The data that support the findings of this study are openly available in the Inter-university Consortium for Political and Social Research at https://doi.org/10.3886/ICPSR27501.v1, reference number 27501.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This material is based upon work supported by the NSF Graduate Research Fellowship (Division of Graduate Education) [grant number DGE-1414475] and NSF under Division of Mathematical Sciences [grant number DMS-1343651].