Ryszard Zieliński’s contribution to statistical optimization and fixed-precision estimation

• Autorzy: Męczarski M.

Identyfikatory

DOI

10.14708/ma.v40i2.378

• Języki publikacji: PL

Abstrakty

EN

Professor Ryszard Zieliński's results in stochastic approximation, extremal experimental design in the framework of response surface analysis and fixed-precision set estimation are outlined. First, he proposed a randomized version of Fabian's (1967) gradient estimate in the Kiefer-Wolfowitz procedure, which reduced the number of required observations and improved the rate of convergence. Second, when considering response surface analysis and experimental designs for the gradient estimation, he constructed a randomized simplex design which resulted in the unbiased estimator. Third, he gave a method to construct confidence sets with prescribed accuracy (i. e. the width and the confidence level) by sampling independent copies of a process of interest. Professor Ryszard Zieliński's results in stochastic approximation, extremal experimental design in the framework of response surface analysis and fixed precision set estimation are outlined. First, he proposed a randomized version of Fabian's (1967) gradient estimate in the Kiefer-Wolfowitz procedure, which reduced the number of required observations and improved the rate of convergence. Second, when considering response surface analysis and experimental designs for the gradient estimation, he constructed a randomized simplex design which resulted in the unbiased estimator. Third, he gave a method to construct confidence sets with prescribed accuracy (i. e. the width and the confidence level) by sampling independent copies of a process of interest.

Słowa kluczowe

EN

stochastic approximation; Kiefer-Wolfowitz procedure; gradient estimation; response surface analysis; simplex design; confidence set; stopping rule; fixed-precision estimation

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Mathematica Applicanda
• Rocznik: 2012
• Tom: Vol. 40, No. 2
• Strony: 107--111
• Opis fizyczny: Bibliogr. 3 poz.

Twórcy

autor

Męczarski M.

Bibliografia

• [1] J. R. Blum, J. Rosenblatt (1969), On fixed precision estimation in time series, Ann. Math. Statist. 40, 1021-1032.
• [2] V. Fabian (1967), Stochastic approximation of minima with improved asymptotic speed, Ann. Math. Statist. 38, 191-200.
• [3] J. Kiefer, J. Wolfowitz (1952), Stochastic estimation of the maximum of a regression function, Ann. Math. Statist. 23, 462-466.