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Prediction intervals and regions for multivariate time series models with sieve bootstrap

Różański R., Chłapiński G., Hławka M., Jamróz K., Kawecki M., Zagdański A.

Probability and Mathematical Statistics

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2018

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Vol. 38, Fasc. 2

317--357

EN

In the paper, the construction of unconditional bootstrap prediction intervals and regions for some class of second order stationary multivariate linear time series models is considered. Our approach uses the sieje bootstrap procedure introduced by Kreiss (1992) and Bühlmann (1997). Basic theoretical results concerning consistency of the bootstrap replications and the bootstrap prediction regions are proved. We present a simulation study comparing the proposed bootstrap methods with the Box-Jenkins approach.

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Complex Formation Equilibria and Potentials of Mn(III)/Mn(II) Couple in the Presence of 1,10-Phenanthroline Derivatives in Aqueous Solutions

Andrijewski G., Nowak L., Tomczyk D., Różański R., Dałkowski R.

Polish Journal of Chemistry

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2006

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Vol. 80, nr 5

693-701

EN

Formation constants ofMn(II) complexes with 5-nitro-, 5-chloro-, 5-methyl-, 4-methyl-, 2,9-dimethyl-, 4,7-dimethyl- and 5,6-dimethyl-1,10-phenanthroline and formal potentials of Mn(III)/Mn(II) couple in the presence of these compounds by use of potentiometric method were determined and used to calculate formation constants of Mn(III) complexeswith these ligands.Anumerical method of manganese(III) complexes formation constants calculation from potentiometric and voltammetric data was proposed and tested for iron(III) complexes. The influence of substituents on protonation and stability constant values was analyzed taking into account suitability of the ligand to stabilize thermodynamically unstableMn(III) ion and protect it from disproportionation.

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On estimation in the multiplicative intensity model via histogram sieve

Różański R., Zagdański A.

Probability and Mathematical Statistics

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2001

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Vol. 21, Fasc. 1

89--99

EN

In the paper we consider the problem of estimating stochastic intensity of a point process from multiplicative intensity model using the method of sieves of Grenander [6]. Basic properties of the histogram sieve estimator including consistency and asymptotic normality are proved. Our approach extends results obtained in Leśkow and Różański [13].

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Transformed diffeomorphic kernel estimation of hazard rate function

Janiszewska B., Różański R.

Demonstratio Mathematica

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2001

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Vol. 34, nr 2

447-460

EN

In the article, a transformed diffeomorphic kernel estimator of the hazard rate function in the presence of censoring is constructed. The estimator is defined in the framework of multiplicative intensity point process model. It is shown that the proposed estimator is asymptotically unbiased, consistent and asymptotically normal. Analysis in the reduction of the bias of the diffeomorphic estimator is carried out. Some simulation results comparing the obtained estimator with the Ramlau-Hansen estimator are also presented.