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Selection in parametric models via some stepdown procedures

100%
Furmańczyk K.
Applicationes Mathematicae
|
2014
|
tom 41
|
nr 1
81-92
EN
The paper considers the problem of consistent variable selection in parametic models with the use of stepdown multiple hypothesis procedures. Our approach completes the results of Bunea et al. [J. Statist. Plann. Inference 136 (2006)]. A simulation study supports the results obtained.
2
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Some remarks on the control of false discovery rate under dependence

100%
Furmańczyk K.
Applicationes Mathematicae
|
2013
|
tom 40
|
nr 3
297-307
EN
We investigate controlling false discovery rate (FDR) under dependence. Our main result is a generalization of the results obtained by Genovese and Wasserman (2004) and Farcomeni (2007).
3
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A uniform central limit theorem for dependent variables

100%
Furmańczyk K.
Applicationes Mathematicae
|
2009
|
tom 36
|
nr 2
129-138
EN
Niemiro and Zieliński (2007) have recently obtained uniform asymptotic normality for the Bernoulli scheme. This paper concerns a similar problem. We show the uniform central limit theorem for a sequence of stationary random variables.
4
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Simultaneous testing procedures of many null hypotheses and their applications in the DNA microarrays analysis

64%
Dudziński M., Furmańczyk K.
Mathematica Applicanda
|
2007
|
tom 35
|
nr 49/08
PL
W naszej pracy rozważamy różne podejścia do problematyki jednoczesnego testowania wielu hipotez zerowych. W tym kontekście omawiamy procedury testowania typu single-step, step-down i step-up. W szczególności, przedstawiamy własności i zastosowania takich miar błędów testowania, jak: FWER, k-FWER, FDP, FDR, pFDR. Wspomniane procedury testowania są intensywnie wykorzystywane w analizie mikromacierzy DNA, która to analiza umożliwia monitorowanie poziomów ekspresji wielu genów jednocześnie oraz znajduje ostatnio szerokie zastosowania w diagnostyce, leczeniu i badaniach medycznych.
EN
In our paper, we consider different approaches to the problem of simultaneous testing of many null hypotheses. In this context, we discuss the single-step, the step-down and the step-up procedures of multiple testing. In particular, we are concerned with their properties and applications in the control of the error rates, such as:FW ER, k-FWER, FDP, FDR, pFDR. The mentioned procedures are intensively used in the DNA microarrays analysis, which enables the monitoring of expression levels of many genes simultaneously and is widely applied in recent medical diagnostics, treatment and research.
5
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A note on control of the false discovery proportion

64%
Dudziński M., Furmańczyk K.
Applicationes Mathematicae
|
2009
|
tom 36
|
nr 4
397-418
EN
We consider the problem of simultaneous testing of a finite number of null hypotheses $H_{i}$, i=1,...,s. Starting from the classical paper of Lehmann (1957), it has become a very popular subject of research. In many applications, particularly in molecular biology (see e.g. Dudoit et al. (2003), Pollard et al. (2005)), the number s, i.e. the number of tested hypotheses, is large and the popular procedures that control the familywise error rate (FWERM) have small power. Therefore, we are concerned with another error rate measure, called the false discovery proportion (FDP). We prove some theorems about control of the FDP measure. Our results differ from those obtained by Lehmann and Romano (2005).
6
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Some applications of the Archimedean copulas in the proof of the almost sure central limit theorem for ordinary maxima

64%
Dudziński M., Furmańczyk K.
Open Mathematics
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2017
|
tom 15
|
nr 1
1024-1034
EN
Our goal is to state and prove the almost sure central limit theorem for maxima (Mn) of X1, X2, ..., Xn, n ∈ ℕ, where (Xi) forms a stochastic process of identically distributed r.v.’s of the continuous type, such that, for any fixed n, the family of r.v.’s (X1, ...,Xn) has the Archimedean copula CΨ.
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