Post-selection inference for linear mixed model parameters using the conditional Akaike information criterion

Gerda Claeskens, Katarzyna Reluga, Stefan Sperlich

Research output: Working paperPreprint

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Abstract

We investigate the issue of post-selection inference for a fixed and a mixed parameter in a linear mixed model using a conditional Akaike information criterion as a model selection procedure. Within the framework of linear mixed models we develop complete theory to construct confidence intervals for regression and mixed parameters under three frameworks: nested and general model sets as well as misspecified models. Our theoretical analysis is accompanied by a simulation experiment and a post-selection examination on mean income across Galicia's counties. Our numerical studies confirm a good performance of our new procedure. Moreover, they reveal a startling robustness to the model misspecification of a naive method to construct the confidence intervals for a mixed parameter which is in contrast to our findings for the fixed parameters.
Original languageEnglish
Publication statusPublished - 22 Sept 2021

Bibliographical note

39 pages, 7 figures

Keywords

  • stat.ME
  • stat.AP
  • stat.CO
  • 62F12, 62F25
  • G.3

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