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Local properties of function fitting estimates with application to system identification. (English) Zbl 0588.62059
Mathematical statistics and applications, Proc. 4th Pannonian Symp. Math. Stat., Bad Tatzmannsdorf/Austria 1983, Vol. B, 141-151 (1985).
[For the entire collection see Zbl 0583.00028.] This paper presents a general family of nonparametric estimates of the unknown function with nonrandom domain. Sufficient conditions for weak and strong pointwise convergence of estimates are derived. A sharper result for the Priestley-Chao kernel estimate is shown. A new consistent sequence of estimates, defined in terms of the k-nearest neighbour (K-NN), is constructed. These results are applied to the problem of identifying noisy linear dynamic systems.

62G05Nonparametric estimation