Koronacki, J.; Wertz, W. Recursive probability density estimation. (Polish. English summary) Zbl 0609.62058 Ann. Soc. Math. Pol., Ser. III, Mat. Stosow. 25, 27-90 (1985). 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 Keywords:survey; asymptotic theory; recursive estimation of probability densities; pointwise properties; asymptotic unbiasedness; consistency; rates of convergence; mean squared error; laws of the iterated logarithm; Berry- Esseen type theorems PDFBibTeX XMLCite \textit{J. Koronacki} and \textit{W. Wertz}, Ann. Soc. Math. Pol., Ser. III, Mat. Stosow. 25, 27--90 (1985; Zbl 0609.62058)