Bin Width Selection in Multivariate Histograms by the Combinatorial Method

• Autores: Luc Devroye , Gábor Lugosi
• Localización: Test: An Official Journal of the Spanish Society of Statistics and Operations Research, ISSN-e 1863-8260, ISSN 1133-0686, Vol. 13, Nº. 1, 2004, págs. 129-145
• Idioma: inglés
• DOI: 10.1007/bf02603004
• Texto completo no disponible (Saber más ...)
• Resumen

  • We present several multivariate histogram density estimates that are universally $L_1$-optimal to within a constant factor and an additive term $O(\sqrt{\log n / n })$. The bin widths are chosen by the combinatorial method developed by the authors in {\it Combinatorial Methods in Density Estimation} (Springer-Verlag, 2001). The present paper solves a problem left open in that book.