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On integer stochastic approximation

Václav DupačUlrich Herkenrath — 1984

Aplikace matematiky

Let M : 𝐑 𝐑 be observable, with experimental errors, at integer points only; unknown elsewhere. Iterative nonparametric procedures for finding the zero point of M are called procedures of integer stochastic approximation. Three types of such procedures (Derman’s, Mukerjee’s and the authors’) are described and compared. A two-dimensional analogue of the third approach is proposed and investigated; its generalization to higher dimensions is conjectured.

Extrapolations in non-linear autoregressive processes

Jiří AndělVáclav Dupač — 1999

Kybernetika

We derive a formula for m -step least-squares extrapolation in non-linear AR ( p ) processes and compare it with the naïve extrapolation. The least- squares extrapolation depends on the distribution of white noise. Some bounds for it are derived that depend only on the expectation of white noise. An example shows that in general case the difference between both types of extrapolation can be very large. Further, a formula for least-squares extrapolation in multidimensional non-linear AR( p ) process is derived....

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