Geodesic
Ryszard Zieliński’s contribution to statistical optimization and fixed-precision estimation
Mathematica Applicanda, Tome 40 (2012) no. 2, pp. 107-111.

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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.
DOI : 10.14708/ma.v40i2.378
Classification : 01A70, 62-03, 62L20, 62K20,62L12, 62L15
Mots-clés : stochastic approximation, Kiefer-Wolfowitz procedure, gradient estimation, response surface analysis, simplex design, confidence set, stopping rule, fixed-precision estimation 
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Marek Męczarski. Ryszard Zieliński’s contribution to statistical optimization and fixed-precision estimation. Mathematica Applicanda, Tome 40 (2012) no. 2, pp.  107-111. doi : 10.14708/ma.v40i2.378. http://geodesic.mathdoc.fr/articles/10.14708/ma.v40i2.378/

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