Frequency Polygons for Random Fields

Michel Carbon
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Michel Carbon: Crest

No 2005-04, Working Papers from Center for Research in Economics and Statistics

Abstract: The purpose of this paper is to investigate the frequency polygon as a densityestimator for stationary random fields indexed by multidimensional lattice pointsspace. Optimal bin widths which asymptotically minimize integrated errors (IMSE)are derived. Under weak conditions, frequency polygons achieve the same rate ofconvergence to zero of the IMSE as kernel estimators. They can also attain theoptimal uniform rate of convergence under general conditions. Frequency polygonsthus appear to be very good density estimators with respect to both criteria of IMSEand uniform convergence.

Pages: 24
Date: 2005
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