  We introduce an efficient and exact algorithm, together with a faster but
approximate version, which implements with a sub-quadratic complexity the
hold-out derived from T-estimation. We study empirically the performance of
this hold-out in the context of density estimation considering well-known
competitors (hold-out derived from least-squares or Kullback-Leibler
divergence, model selection procedures, etc.) and classical problems including
histogram or bandwidth selection. Our algorithms are integrated in a companion
R-package called {\it Density.T.HoldOut} available on the CRAN:
{\url{http://cran.r-project.org/web/packages/Density.T.HoldOut/index.html}}.
