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

Marek 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 -