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Global convergence of the recursive kernel regression estimates with applications in classification and nonlinear system estimation

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1 Author(s)
A. Krzyzak ; Dept. of Comput. Sci., Concordia Univ., Montreal, Que., Canada

An improved exponential bound on the L1 error for the recursive kernel regression estimates is derived. It is shown, using the martingale device, that weak, strong and complete L 1 consistencies are equivalent. Consequently the conditions on a certain smoothing sequence are necessary and sufficient for strong L1 consistency of the recursive kernel regression estimate. The rates of global convergence are also given. Obtained results are applied to recursive classification rules and to nonlinear time series estimation

Published in:

IEEE Transactions on Information Theory  (Volume:38 ,  Issue: 4 )