Local convergence theorems for adaptive stochastic approximation schemes | Zendy

Tze Leung Lai | Zendy; Herbert Robbins | Zendy

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Local convergence theorems for adaptive stochastic approximation schemes

Author(s) -

Tze Leung Lai,

Herbert Robbins

Publication year - 1979

Publication title -

proceedings of the national academy of sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 5.011

H-Index - 771

eISSN - 1091-6490

pISSN - 0027-8424

DOI - 10.1073/pnas.76.7.3065

Subject(s) - limiting , convergence (economics) , stochastic approximation , mathematics , regression function , convergence of random variables , rate of convergence , regression , function (biology) , combinatorics , random variable , discrete mathematics , statistics , computer science , economics , biology , mechanical engineering , computer network , channel (broadcasting) , computer security , key (lock) , engineering , economic growth , evolutionary biology

For the regression model y = M(x) + epsilon, adaptive stochastic approximation schemes of the form x(n+1) = x(n) - y(n)/(nb(n)) for choosing the levels x(1),x(2),... at which y(1),y(2),... are observed converge with probability 1 to the unknown root theta of the regression function M(x). Certain local convergence theorems that relate the convergence rate of x(n) - theta to the limiting behavior of the random variables b(n) are established.

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