'Which model?' is the wrong question

Abstract

A perspective is presented in which the search for a suitable model on which to base inferential statements related to the analysed dataset is not useful and leads, with the established practice, to invalid statements. Composition is proposed as an alternative, in which the candidate estimators are (linearly) combined. Three generic examples are discussed: the analysis of variance in which model selection is a direct cause of inefficiency, clinical trials (experiments) in which model selection is not practiced and small-area estimation in which one aspect of model selection has been dismissed decisively a long time ago, and there are more effective criteria for the other aspects of the problem. © 2012 The Author. Statistica Neerlandica © 2012 VVS.