UPPER BOUNDS ON THE MINIMUM COVERAGE PROBABILITY OF CONFIDENCE INTERVALS IN REGRESSION AFTER MODEL SELECTION

摘要: Summary We consider a linear regression model, with the parameter of interest specified combination components vector. We suppose that, as first step, data-based model selection (e.g. by preliminary hypothesis tests or minimizing Akaike information criterion – AIC) is used to select model. It common statistical practice then construct confidence interval for interest, based on assumption that selected had been given us a priori. This false, and it can lead poor coverage properties. provide an easily computed finite-sample upper bound (calculated repeated numerical evaluation double integral) minimum probability this interval. applies any following methods: AIC, Bayesian (BIC), maximum adjusted R2, Mallows' CP and t-tests. The importance delineates general categories design matrices procedures which has shown be analogue earlier large-sample due Kabaila Leeb.