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Robust estimation of the scale and weighted distributions

100%
Błażej P.
Applicationes Mathematicae
|
2007
|
tom 34
|
nr 1
29-38
EN
The concept of robustness given by Zieliński (1977) is considered in cases where violations of models are generated by weight functions. Uniformly most bias-robust estimates of the scale parameter, based on order statistics, are obtained for some statistical models. Extensions of results of Zieliński (1983) and Bartoszewicz (1986) are given.
2
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Robust estimation based on spacings in weighted exponential models

63%
Błażej P., Bartoszewicz J.
Applicationes Mathematicae
|
2007
|
tom 34
|
nr 4
405-411
EN
Using Zieliński's (1977, 1983) formalization of robustness Błażej (2007) obtained uniformly most bias-robust estimates (UMBREs) of the scale parameter for some statistical models (including the exponential model), in a class of linear functions of order statistics, when violations of the models are generated by weight functions. In this paper the UMBRE of the scale parameter, based on spacings, in two weighted exponential models is derived. Extensions of results of Bartoszewicz (1986, 1987) are given.
3
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Two algorithms based on Markov chains and their application to recognition of protein coding genes in prokaryotic genomes

51%
Grabińska M., Błażej P., Mackiewicz P.
Applicationes Mathematicae
|
2013
|
tom 40
|
nr 4
447-457
EN
Methods based on the theory of Markov chains are most commonly used in the recognition of protein coding sequences. However, they require big learning sets to fill up all elements in transition probability matrices describing dependence between nucleotides in the analyzed sequences. Moreover, gene prediction is strongly influenced by the nucleotide bias measured by e.g. G+C content. In this paper we compare two methods: (i) the classical GeneMark algorithm, which uses a three-periodic non-homogeneous Markov chain, and (ii) an algorithm called PMC that considers six independent homogeneous Markov chains to describe transition between nucleotides separately for each of three codon positions in two DNA strands. We have tested the efficiency (in terms of true positive rate) of these two Markov chain methods for the model bacterial genome of Escherichia coli depending on the size of the learning set, uncertainty of ORFs' function annotation, and model order of these algorithms. We have also applied the methods with different model orders for 163 prokaryotic genomes that covered a wide range of G+C content. The PMC algorithm of different chain orders turns out to be more stable in comparison to the GeneMark algorithm. The PMC also outperforms the GM algorithm giving a higher fraction of coding sequences in the tested set of annotated genes. Moreover, it requires much smaller learning sets than GM to work properly.
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