{"paper":{"title":"Upper bounds on the minimum coverage probability of confidence intervals in regression after variable selection","license":"","headline":"","cross_cats":["stat.AP","stat.TH"],"primary_cat":"math.ST","authors_text":"Khageswor Giri, Paul Kabaila","submitted_at":"2007-11-07T01:38:37Z","abstract_excerpt":"We consider a linear regression model, with the parameter of interest a specified linear combination of the regression parameter vector. We suppose that, as a first step, a data-based model selection (e.g. by preliminary hypothesis tests or minimizing AIC) is used to select a model. It is common statistical practice to then construct a confidence interval for the parameter of interest based on the assumption that the selected model had been given to us a priori. This assumption is false and it can lead to a confidence interval with poor coverage properties. We provide an easily-computed finite"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0711.0993","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}