Stochastic approximation / M. T. WasanType de document : MonographieCollection : Cambridge tracts in mathematics and mathematical physics, 58Langue : anglais.Pays : Grande Bretagne.Éditeur : Cambridge : Cambridge University Press, 1969Description : 1 vol. (X-202 p.) ; 23 cmISBN : 9780521073684.ISSN : 0068-6824.Bibliographie : Bibliogr. p. 195-199. Index.Sujet MSC : 62L20, Sequential statistical methods, Stochastic approximation
62-02, Research exposition (monographs, survey articles) pertaining to statisticsEn-ligne : Google édition 2004 | MathSciNet
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Bibliogr. p. 195-199. Index
From the author's introduction: "In Chapter 2 the Robbins-Monro method is described for a particular applied problem of response-no-response analysis. Then a general one-dimensional stochastic approximation is investigated. It is shown that when one has some knowledge of the process one can relax conditions. For example, if it is known only that the stochastic-approximation sequence is regular, the conditions imposed on the iterating coefficients can be relaxed. A small sample theory is discussed and comparison is made with the asymptotic one. Then many modifications of a general case are mentioned which have revealing effect on the stochastic-approximation procedures.
"Chapter 3 discusses a method of Kiefer and Wolfowitz for determining the location of a maximum of a regression function, and singles out the optimum choice of iterating coefficients. A unified treatment of the subject of Chapters 2 and 3 is given and a procedure for obtaining the location of an inflection point is stated. For a simple regression model, a stochastic-approximation technique is exploited with advantage.
"Chapter 4 shows how a method of stochastic approximation can be used in a control problem and its difference from the conventional procedure. Then a problem of pharmacology is discussed. Its application to a reliability situation indicates how such a method is effective in measuring information. Its uses in problems of bioassay are investigated.
"In Chapter 5 a multivariate stochastic-approximation procedure is introduced and its utility in the investigation of a kinetic model of pharmacology is discussed.
"Chapter 6 deals with the problem of asymptotic distribution and exploits a method of moments and a characteristic function method. An application to the construction of confidence interval is indicated.
"In Chapter 7 the techniques of stochastic approximation for continuous random processes are dealt with and their utility for analogue computers is stated. Their applications to a control problem, and a filter problem are discussed.
"In Chapter 8 an `up-and-down' method is investigated and its application to `Rankits' is shown. Small sample and non-parametric up-and-down methods are appended.
"Appendices on the subjects of iterative techniques, limit theorems and inequalities are also added.
"The problems at the end of each chapter provide additional information which is obtainable from the references.''