ISSN:
1588-2829
Keywords:
Primary 60F15, 62G05
;
Secondary 41A30, 41A36, 62G99, 62L20
;
Density estimation
;
strong laws
;
approximation by Bernstein polynomials
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract Starting from the classical theorem of Weierstrass (and its modifications) on approximation of continuous functions by means of Bernstein polynomials a smoothed histogram type estimator is developed for estimating probability densities and its derivatives. Consistency results are obtained in form of various strong laws. In particular, one gets estimates for the rates for pointwise and uniform strong convergence of estimators for the derivatives. Moreover, for approximating the density itself the exact order of consistency is established. This is done by a law of iterated logarithm for pointwise approximation and by a law of logarithm in case of uniform approximation.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01855801
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