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

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