Polygone des fréquences pour des champs aléatoires

Abstract

The purpose of this Note is to investigate the frequency polygon as a density estimator for stationary random fields indexed by multidimensional lattice points space. Optimal bin widths which asymptotically minimize integrated errors (IMSE) are derived. Under mild regularity assumptions, frequency polygons achieve the same rate of convergence to zero of the IMSE as kernel estimators. They can also attain the rate of uniform convergence under general conditions. Frequency polygons thus appear to be very good density estimators with respect to both criteria of IMSE and uniform convergence. To cite this article: M. Carbon, C. R. Acad. Sci. Paris, Ser. I 342 (2006).