×

Recursive probability density estimation. (Polish. English summary) Zbl 0609.62058

A survey of the asymptotic theory of recursive estimation of probability densities is given. Stress is laid on pointwise properties. In particular, asymptotic unbiasedness and consistency under possibly minimal assumptions and the rates of convergence of the mean squared error, laws of the iterated logarithm and Berry-Esseen type theorems under suitably stronger assumptions are discussed for the estimators in question.
The paper is a slightly modified version of an earlier paper of the second author in R. Zieliński (ed.), Sequential methods in statistics. Banach Center Publications, 16.

MSC:

62G05 Nonparametric estimation
62E20 Asymptotic distribution theory in statistics
60F15 Strong limit theorems
60F17 Functional limit theorems; invariance principles
PDFBibTeX XMLCite