Inferential models for linear regression

Zuoyi Zhang, Huiping Xu, Ryan Martin, Chuanhai Liu

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

Linear regression is arguably one of the most widely used statistical methods. However, important problems, especially variable selection, remain a challenge for classical modes of inference. This paper develops a recently proposed framework of inferential models (IMs) in the linear regression context. In general, the IM framework is able to produce meaningful probabilistic summaries of the statistical evidence for and against assertions about the unknown parameter of interest, and these summaries are shown to be properly calibrated in a frequentist sense. Here we demonstrate by example that the IM framework is promising for linear regression analysis---including model checking, variable selection, and prediction---and for uncertain inference in general.

Original languageEnglish
Pages (from-to)413-432
Number of pages20
JournalPakistan Journal of Statistics and Operation Research
Volume7
Issue number2 SPECIAL ISSUE
StatePublished - Oct 2011

Fingerprint

Linear regression
Variable Selection
Model checking
Assertion
Regression Analysis
Regression analysis
Unknown Parameters
Statistical method
Model Checking
Statistical methods
Model
Prediction
Demonstrate
Framework
Variable selection
Inference

Keywords

  • Auxiliary variable
  • Credibility
  • Prediction
  • Predictive random set
  • Variable selection

ASJC Scopus subject areas

  • Management Science and Operations Research
  • Statistics, Probability and Uncertainty
  • Modeling and Simulation
  • Statistics and Probability

Cite this

Zhang, Z., Xu, H., Martin, R., & Liu, C. (2011). Inferential models for linear regression. Pakistan Journal of Statistics and Operation Research, 7(2 SPECIAL ISSUE), 413-432.

Inferential models for linear regression. / Zhang, Zuoyi; Xu, Huiping; Martin, Ryan; Liu, Chuanhai.

In: Pakistan Journal of Statistics and Operation Research, Vol. 7, No. 2 SPECIAL ISSUE, 10.2011, p. 413-432.

Research output: Contribution to journalArticle

Zhang, Z, Xu, H, Martin, R & Liu, C 2011, 'Inferential models for linear regression', Pakistan Journal of Statistics and Operation Research, vol. 7, no. 2 SPECIAL ISSUE, pp. 413-432.
Zhang Z, Xu H, Martin R, Liu C. Inferential models for linear regression. Pakistan Journal of Statistics and Operation Research. 2011 Oct;7(2 SPECIAL ISSUE):413-432.
Zhang, Zuoyi ; Xu, Huiping ; Martin, Ryan ; Liu, Chuanhai. / Inferential models for linear regression. In: Pakistan Journal of Statistics and Operation Research. 2011 ; Vol. 7, No. 2 SPECIAL ISSUE. pp. 413-432.
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