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1

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

Męczarski M.

Mathematica Applicanda

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2012

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Vol. 40, No. 2

107--111

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.

2

Remarks on Statistical Design Centering

Opalski L. J.

International Journal of Electronics and Telecommunications

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2011

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Vol. 57, No. 2

159-167

EN

The paper overviews optimization based statistical design centering techniques for analog circuits. Emphasis is placed on dependence between formulation of quality indices, problem formulation, and computational complexity of design centering algorithms, executed in single- or multiple-processor environments. For characterization of solution techniques a standard CMOS op-amp design case and a simplified computational complexity analysis are used.

3

Pewne uwagi o aproksymacji stochastycznej krzywych narastania liczby pęknięć drutów lin nośnych wyciągów szybowych

Czaplicki J.

Zeszyty Naukowe. Górnictwo / Politechnika Śląska

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2007

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z. 280

241-254

PL

Procesy kumulacji liczby pęknięć drutów lin nośnych wyciągów szybowych charakteryzuje właściwość dość regularnego układania się wartości empirycznych wzdłuż rosnących krzywych, przede wszystkim w początkowej fazie procesu użytkowania lin. Procesy te stały się ostatnio ponownym obiektem badań empiryczno-teoretycznych. Stale istotnym problemem jest zagadnienie jak najlepszego opisu matematycznego danych kopalnianych. Są to zagadnienia z zakresu aproksymacji stochastycznej. W pracy sformułowano zagadnienie wyboru funkcji opisującej dane empiryczne, rozważono warunki szacowania parametrów strukturalnych funkcji oraz przedyskutowano kilka przykładowych, stosowanych funkcji aproksymacyjnych.

EN

Process of wire crack accumulation running during process of exploitation of steel ropes in shaft hoists possesses property of regular arrangement along increasing curves, especially at the primary stage of rope utilization. Taking into account that these processes became again the point of consideration in research works, it is worth to consider the problem how to find the best mathematical description for mine data. The problem belongs to the stochastic approximation scope of consideration. In the paper the problem of selection of function that describe well empirical data was formulated, its mathematical conditions were taken into account and some basic functions usually applied were considered.

4

Simultaneous Perturbation Stochastic Approximation in global optimisation

Patan K.

Prace Naukowe Politechniki Warszawskiej. Elektronika

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2006

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z. 156

343-350

EN

The paper deals with global property analysis of the Simultaneous Perturbation Stochastic Approximation algorithm. It spite of the fact that the algorithm uses an estimation of a gradient, a global optimisation property can be achieved by using properly shaped sequence {ck} used for generating trial points. The experiments are performed on a number of test functions showing efficiency of the method. The examined algorithm is also used to train a dynamic neural network. A network under consideration is designed using neuron models with internal dynamice. The identification of an industrial process based on real data shows usefullness of the algorithm.

5

Dependent noise for stochastic algorithms

Doukhan P., Brandierie O.

Probability and Mathematical Statistics

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2004

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Vol. 24, Fasc. 2

381--399

EN

We introduce different ways of being dependent for the input noise of stochastic algorithms. We are aimed to prove that such innovations allow to use the ODE (ordinary differential equation) method. Illustrations to the linear regression frame and to the law of large numbers for triangular arrays of weighted dependent random variables are also given.