Upper expectation parametric regression

Lu Lin, Ping Dong, Yunquan Song, Lixing Zhu

Research output: Contribution to journalJournal articlepeer-review

8 Citations (Scopus)


In regression analysis, some predictors might be unobservable, not observed, or ignored. These factors actually a ect the response randomly. The observed data thus follows a conditional distribution when these factors are given. This phenomenon is called the distribution randomness. For such a working model, we propose an upper expectation regression and a two-step penalized maximum least squares procedure to estimate parameters in the mean function and the upper expectation of the error. The resulting estimators are consistent and asymptotically normal under certain conditions. Simulation studies and a data example are used to show that the classical least squares estimation fails but the proposed estimation performs well.

Original languageEnglish
Pages (from-to)1265-1280
Number of pages16
JournalStatistica Sinica
Issue number3
Publication statusPublished - Jul 2017

Scopus Subject Areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

User-Defined Keywords

  • Distribution randomness
  • Penalized least squares
  • Upper expectation


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