In statistical analysis, Freedman's paradox, named after David Freedman

David A. Freedman (statistician)

David A. Freedman was Professor of Statistics at the University of California, Berkeley. He was a distinguished mathematical statistician whose wide-ranging research included the analysis of martingale inequalities, Markov processes, de Finetti's theorem, consistency of Bayes estimators, sampling,...

, describes a problem in model selection

Model selection

Model selection is the task of selecting a statistical model from a set of candidate models, given data. In the simplest cases, a pre-existing set of data is considered...

 whereby predictor variables

Dependent and independent variables

The terms "dependent variable" and "independent variable" are used in similar but subtly different ways in mathematics and statistics as part of the standard terminology in those subjects...

 with no explanatory power can appear artificially important. Freedman demonstrated (through simulation and asymptotic calculation) that this is a common occurrence when the number of variables is similar to the number of data points. Recently, new information-theoretic

Information theory

Information theory is a branch of applied mathematics and electrical engineering involving the quantification of information. Information theory was developed by Claude E. Shannon to find fundamental limits on signal processing operations such as compressing data and on reliably storing and...

estimators have been developed in an attempt to reduce this problem, in addition to the accompanying issue of model selection bias, whereby estimators of predictor variables that have a weak relationship with the response variable are biased.