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

Mathematica Applicanda (2012)

- Volume: 40, Issue: 2
- ISSN: 1730-2668

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topMarek Męczarski. "Ryszard Zieliński’s contribution to statistical optimization and fixed-precision estimation." Mathematica Applicanda 40.2 (2012): null. <http://eudml.org/doc/292560>.

@article{MarekMęczarski2012,

abstract = {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 prescribedaccuracy (i. e. the width and the confidence level) by sampling independent copiesof a process of interest.},

author = {Marek Męczarski},

journal = {Mathematica Applicanda},

keywords = {stochastic approximation, Kiefer-Wolfowitz procedure, gradient estimation, response surface analysis, simplex design, confidence set, stopping rule, fixed-precision estimation},

language = {eng},

number = {2},

pages = {null},

title = {Ryszard Zieliński’s contribution to statistical optimization and fixed-precision estimation},

url = {http://eudml.org/doc/292560},

volume = {40},

year = {2012},

}

TY - JOUR

AU - Marek Męczarski

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

JO - Mathematica Applicanda

PY - 2012

VL - 40

IS - 2

SP - null

AB - 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 prescribedaccuracy (i. e. the width and the confidence level) by sampling independent copiesof a process of interest.

LA - eng

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

UR - http://eudml.org/doc/292560

ER -

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