Open AccessFrequency polygons for random fields (density estimation for random fields)
Author(s) -
Michel Carbon
Publication year - 2007
Publication title -
revista de matemáticas
Language(s) - English
Resource type - Journals
eISSN - 2215-3373
pISSN - 1409-2433
DOI - 10.15517/rmta.v14i2.39304
Subject(s) - estimator , mathematics , polygon (computer graphics) , rate of convergence , kernel density estimation , random field , convergence (economics) , uniform convergence , kernel (algebra) , mathematical optimization , mathematical analysis , bandwidth (computing) , statistics , combinatorics , computer science , telecommunications , computer network , channel (broadcasting) , frame (networking) , economics , economic growth
The purpose of this paper 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 weak conditions, frequency polygons achieve the same rate of convergence to zero of the IMSE as kernel estimators. They can also attain the optimal uniform rate of convergence under general conditions. Frequency polygons thus appear to be very good density estimators with respect to both criteria of IMSE and uniform convergence.