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On a coefficient of uncertainty based on the condition number of the matrix of observations

Grzybowski A.

Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej

2007

Vol. 6, nr 1

69-74

The paper is devoted to the problem of incorporating prior information into regression model estimation. We assume the prior information about regression parameter is derived from regression analysis applied to some phenomenon described by the same regression equation. However, usually the prior information is uncertain. On the base of computer simulation we construct a coefficient which allows incorporating the prior information along with its uncertainty. The coefficient is based upon the index number of the matrix of observations of the explanatory variables. Performance of estimators based upon the coefficient of uncertainty is examined through computer simulations.

On some new method of incorporation prior information along with its uncertainty in regression estimation

Grzybowski A. Z.

Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej

2006

Vol. 5, nr 1

23-31

The paper is devoted to the problem of incorporating prior information in the regression estimation. In series of papers, see [3-6], we have proposed and analyzed some model of uncertainty which allow incorporating prior information along with its uncertainty via some Bayes estimators. We also introduced the notion of an Index of Uncertainty (IU) which indicate how useful the information and consequently the proposed estimators are. The results and methodology are summarized in [7]. Here, assuming different than in the mentioned papers prior knowledge about the regression problems, we propose a new description of uncertainty along with an index of uncertainty which was developed on the base of computer simulation.

Asking price model for used car market - incorporating prior information

Grzybowski A.

Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej

2005

Vol. 4, nr 1

50-57

The paper is devoted to the problem of a choice between various regression models for asking price of used cars. Different models can be obtained with the help of different estimators which can be adopted during the process of identification of model parameters. We compare models obtained using prior information with the ones obtained with the help of ignoring the information LS-estimator.