Stochastic Systems

Necessary and sufficient conditions for convergence with probability 1 of kernel estimates of a probability density and its derivatives

M. O. Ioffe, V. Ya. Katkovnik

Leningrad

Abstract: The necessary and sufficient conditions are provided for convergence almost surely of kernel estimates of the probability density. For a specific range of estimates a repeated logarithm is obtained which leads to an accurate characteristic of the asymptotic rate of convergence almost surely. The findings are extended to estimates of probability density derivatives.

UDC: 519.272


Received: 04.06.1985

 English version: Automation and Remote Control, 1986, 47:12, 1632–1641

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