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Confidence sets for a level set in linear regression.

Fang Wan1, Wei Liu2, Frank Bretz3

  • 1Department of Mathematics and Statistics, Lancaster University, Bilrigg lane, Lancaster, LA1 4YF, UK.

Statistics in Medicine
|January 6, 2024
PubMed
Summary
This summary is machine-generated.

This study introduces a new method for constructing confidence sets for regression level sets in linear models. The approach is widely applicable to various parametric regression models, enhancing statistical analysis.

Keywords:
confidence setslinear regressionnonparametric regressionparametric regressionsimultaneous confidence bandsstatistical inference

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Area of Science:

  • Statistics
  • Statistical Modeling

Background:

  • Traditional regression analysis focuses on estimating the regression function.
  • Recent focus shifts to estimating the level set, defined by covariate values where the regression function exceeds a threshold.
  • Existing research primarily addresses nonparametric regression and point estimation.

Purpose of the Study:

  • To develop confidence sets for the level set in linear regression analysis.
  • To extend the methodology to other parametric regression models.

Main Methods:

  • Construction of upper, lower, and two-sided confidence sets for normal-error linear regression.
  • Utilizing simultaneous confidence bands for confidence set construction.
  • Demonstrating applicability to generalized linear models, linear mixed models, and generalized linear mixed models.

Main Results:

  • Confidence sets for linear regression level sets can be easily constructed from simultaneous confidence bands.
  • The proposed construction method is broadly applicable to various parametric regression models with monotonic link functions.
  • Simulation studies and real examples validate the method's effectiveness.

Conclusions:

  • The developed method provides a practical approach for constructing confidence sets for regression level sets.
  • The wide applicability of the method across different parametric models offers significant advantages for statistical inference.
  • This work advances the estimation of regression level sets beyond point estimation.