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1

An Explicit Characterization of Admissible Linear Estimators of Fixed and Random Effects in Balanced Random Models

Synówka-Bejenka Ewa, Zontek Stefan

Probability and Mathematical Statistics

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2020

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Vol. 40, Fasc. 1

105--118

EN

A necessary and sufficient conditions for a linear estimator of a linear function of fixed and random effects in a balanced random model to be admissible are given. The formulae for admissible estimators depend on certain coefficients from the interval [0, 1], as in well-known results for other models (see e.g. Cohen [3]).

2

Wpływ parametrów powietrza płynącego przez parownik oraz chłodnicę wyparną wody na moc chłodniczą chłodziarki TS-300B

Nowak B., Kuczera Z., Łuczak R., Ptaszyński B., Życzkowski P.

Wiadomości Górnicze

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2014

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R. 65, nr 12

630--638

PL

W artykule przedstawiono równania kryterialne umożliwiające określenie mocy cieplnej parownika chłodziarki powietrza TS-300B współpracującej z wyparną chłodnicą wody CWW-420. Do ich utworzenia wykorzystano statystyczne metody estymacji liniowej i nieliniowej danych otrzymanych z numerycznych rozwiązań równań opisujących rzeczywiste procesy zachodzące w chłodziarkach bezpośredniego działania współpracujących z wyparnymi chłodnicami wody. Do wszystkich równań kryterialnych przeprowadzono ich weryfikację. Polegała ona na określeniu bezwzględnych i względnych odchyłek wartości mocy cieplnych parownika chłodziarki TS-300B wynikających z poszczególnych kryteriów od wartości obliczonych z numerycznego rozwiązania modelu pracy rozważanego lokalnego systemu chłodzenia powietrza.

EN

The article presents the criteria equation allowing determining the thermal capacity of the evaporator of TS-300B air cooler, cooperating with CWW-420 evaporating water cooler. The statistical methods were used of linear and nonlinear estimation of the data obtained from numerical solutions of equations describing the actual processes taking place in the coolers of direct operation, cooperating with evaporative water coolers. For all criteria equations their verification was carried out. It consisted in the determination of absolute and relative deviations of the thermal power value of the evaporator of the TS-300B cooler arising from the specific individual criteria from the values calculated by the numerical solution of the wok model related to local air cooling system under consideration.

3

State estimate based control design using the unified algebraic approach

Filasova A., Krokavec D.

Archives of Control Sciences

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2010

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Vol. 20, no. 1

5-18

EN

The LMI based method for the control with the state estimate, subject to the input variable constraints in the state feedback control of the linear MIMO systems, is presented in the paper. For this problem are obtained the state feedback as well as the estimator gain matrices that capture the required stability by solving the linear matrix inequalities formulated in the sense of the unified algebraic approach. The method is particularly effective when the input variable constraints and the system output are of interest.

4

Geometry of linear and quadratic estimation in a normal linear model with singular variance-covariance matrix

Stępniak Cz.

Demonstratio Mathematica

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1999

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Vol. 32, nr 3

639-645

EN

Many statistical problems, among others those involving restrains on parameters, lead to the models with singular variance-covariance matrix. It is shown that the problems can be reduced to the same problems in the standard linear model.

5

Une étude algébrique de l’admissibilité en estimation linéaire de la moyenne sur un modéle général de Gauss-Markov

Téchené Jean-Jacques

Probability and Mathematical Statistics

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1998

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Vol. 18, Fasc. 2

219--245

EN

It would appear useful to come back to the question of admissibility in linear estimation on a general Gauss-Markov model. We prove how a functional approach to this problem, based on a very important LaMotte theorem [11], clearly leads to characterization of all admissible linear estimators of mean vector or linear transformation of mean vector. Thus we have managed to modify significantly a Klonecki and Zontek theorem [9] allowing us to find in a different way an essential characterization shown by Baksalary and Markiewicz [4], based on the logic put forward by Rao (cf. [13] and [14]). We also give a variational characterization of admissibility in linear estimation and a geometrical proof of a Baksalary and Mathew theorem [7] relative to equality between the set of best linear unbiased estimators (or Gauss-Markov estimators) and the set of linear admissible estimators of mean vector. We finish by explaining more results on admissibility of linear estimators of vector parameters.