A mixed model approach to measurement error in semiparametric regression

Mohammad W. Hattab, David Ruppert

Research output: Contribution to journalArticlepeer-review

Abstract

An essential assumption in traditional regression techniques is that predictors are measured without errors. Failing to take into account measurement error in predictors may result in severely biased inferences. Correcting measurement-error bias is an extremely difficult problem when estimating a regression function nonparametrically. We propose an approach to deal with measurement errors in predictors when modelling flexible regression functions. This approach depends on directly modelling the mean and the variance of the response variable after integrating out the true unobserved predictors in a penalized splines model. We demonstrate through simulation studies that our approach provides satisfactory prediction accuracy largely outperforming previously suggested local polynomial estimators even when the model is incorrectly specified and is competitive with the Bayesian estimator.

Original languageEnglish (US)
Article number31
JournalStatistics and Computing
Volume31
Issue number3
DOIs
StatePublished - May 2021

Keywords

  • Nonparametric regression
  • Penalized splines
  • Variance function estimation

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Computational Theory and Mathematics

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