Nonlinear regression models for heterogeneous data with massive outliers

Research output: Contribution to journalArticle

Abstract

The income or expenditure-related data sets are often nonlinear, heteroscedastic, skewed even after the transformation, and contain numerous outliers. We propose a class of robust nonlinear models that treat outlying observations effectively without removing them. For this purpose, case-specific parameters and a related penalty are employed to detect and modify the outliers systematically. We show how the existing nonlinear models such as smoothing splines and generalized additive models can be robustified by the case-specific parameters. Next, we extend the proposed methods to the heterogeneous models by incorporating unequal weights. The details of estimating the weights are provided. Two real data sets and simulated data sets show the potential of the proposed methods when the nature of the data is nonlinear with outlying observations.

Original languageEnglish
Pages (from-to)1456-1477
Number of pages22
JournalJournal of Applied Statistics
Volume46
Issue number8
DOIs
Publication statusPublished - 2019 Jun 11

Keywords

  • Case-specific parameters
  • generalized additive models
  • heteroscedasticity
  • nonlinear regression
  • outliers
  • robust regression

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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