A general framework for frequentist model averaging

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review

11 Scopus Citations
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Author(s)

  • Priyam Mitra
  • Heng Lian
  • Ritwik Mitra
  • Hua Liang
  • Min-ge Xie

Related Research Unit(s)

Detail(s)

Original languageEnglish
Pages (from-to)205-226
Journal / PublicationScience China Mathematics
Volume62
Issue number2
Online published16 Jan 2019
Publication statusPublished - Feb 2019

Abstract

Model selection strategies have been routinely employed to determine a model for data analysis in statistics, and further study and inference then often proceed as though the selected model were the true model that were known a priori. Model averaging approaches, on the other hand, try to combine estimators for a set of candidate models. Specifically, instead of deciding which model is the `right' one, a model averaging approach suggests to fit a set of candidate models and average over the estimators using data adaptive weights. In this paper we establish a general frequentist model averaging framework that does not set any restrictions on the set of candidate models. It broadens the scope of the existing methodologies under the frequentist model averaging development. Assuming the data is from an unknown model, we derive the model averaging estimator and study its limiting distributions and related predictions while taking possible modeling biases into account. We propose a set of optimal weights to combine the individual estimators so that the expected mean squared error of the average estimator is minimized. Simulation studies are conducted to compare the performance of the estimator with that of the existing methods. The results show the benefits of the proposed approach over traditional model selection approaches as well as existing model averaging methods.

Research Area(s)

  • asymptotic distribution, bias variance trade-off, local mis-specification, model averaging estimators, optimal weight selection

Citation Format(s)

A general framework for frequentist model averaging. / Mitra, Priyam; Lian, Heng; Mitra, Ritwik et al.
In: Science China Mathematics, Vol. 62, No. 2, 02.2019, p. 205-226.

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review