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  • Open Daily: 10am - 10pm
    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
3038 Hennepin Ave Minneapolis, MN
612-822-4611
Stochastic Approximation and NonLinear Regression

Stochastic Approximation and NonLinear Regression

Albert, Arthur E.
Gardner, Leland A.

Paperback

Series: MIT Press Classics

General Science

ISBN10: 0262511487
ISBN13: 9780262511483
Publisher: Mit Pr
Published: Mar 17 2003
Pages: 222
Weight: 0.70
Height: 0.50 Width: 5.90 Depth: 8.90
Language: English

This monograph addresses the problem of real-time curve fitting in the presence of noise, from the computational and statistical viewpoints. It examines the problem of nonlinear regression, where observations are made on a time series whose mean-value function is known except for a vector parameter. In contrast to the traditional formulation, data are imagined to arrive in temporal succession. The estimation is carried out in real time so that, at each instant, the parameter estimate fully reflects all available data. Specifically, the monograph focuses on estimator sequences of the so-called differential correction type. The term differential correction refers to the fact that the difference between the components of the updated and previous estimators is proportional to the difference between the current observation and the value that would be predicted by the regression function if the previous estimate were in fact the true value of the unknown vector parameter. The vector of proportionality factors (which is generally time varying and can depend upon previous estimates) is called the gain or smoothing vector. The main purpose of this research is to relate the large-sample statistical behavior of such estimates (consistency, rate of convergence, large-sample distribution theory, asymptotic efficiency) to the properties of the regression function and the choice of smoothing vectors. Furthermore, consideration is given to the tradeoff that can be effected between computational simplicity and statistical efficiency through the choice of gains.

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