This is the second talk in the RSS Northern Ireland Seminar Series for 2022.
Most powerful inference after model selection.
Gerda Claeskens, The Catholic University of Leuven, Belgium, EU.
Classical - textbook - inference assumes that a model that is used for inference is correct and given before the analysis. Statistical practice, however, includes variable selection and model selection steps before arriving at the inference part. When confidence intervals or hypothesis tests are to be constructed for parameters in a selected model, most likely misspecified, the classical formulas no longer apply in the sense that computed p-values via classical formulas are smaller than they actually are and confidence intervals are too narrow for the intended nominal coverage. The main starting point of selective inference is to condition on the event of having selected the model that one wishes to use for inference. As a tool for valid inference in this talk confidence distributions are used, conditional on the event of having selected a model.
Under some assumptions, uniformly most powerful post-selection confidence curves are obtained.
This is joint work with Andrea Garcia-Angulo.
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