Density estimation using game theory

In this note we show that the mathematical tools of cooperative game theory allow a successful approach to the statistical problem of estimating a density function. Specifically, any random sample of an absolutely continuous random variable determines a transferable utility game, the Shapley value of which proves to be an estimator of the density function of binned kernel and WARPing types, with good computational and statistical properties.Authors acknowledge the financial support of Spanish Ministry for Science and Technology and FEDER through projects BFM2002-03213 and BEC2002-04102-C02-02 and of Xunta de Galicia through projects PGIDT00PXI20104PR and PGIDT03PXIC20701PN. They also thank the comments of two anonymous referees.