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Controlling the effect of multiple testing in Big Data

100%
Denkowska S.
Mathematical Economics
|
2014
|
issue 10(17)
5-16
EN
Big Data poses a new challenge to statistical data analysis. An enormous growth of available data and their multidimensionality challenge the usefulness of classical methods of analysis. One of the most important stages in Big Data analysis is the verification of hypotheses and conclusions. With the growth of the number of hypotheses, each of which is tested at  significance level, the risk of erroneous rejections of true null hypotheses increases. Big Data analysts often deal with sets consisting of thousands, or even hundreds of thousands of inferences. FWER-controlling procedures recommended by Tukey [1953], are effective only for small families of inferences. In cases of numerous families of inferences in Big Data analyses it is better to control FDR, that is the expected value of the fraction of erroneous rejections out of all rejections. The paper presents marginal procedures of multiple testing which allow for controlling FDR as well as their interesting alternative, that is the joint procedure of multiple testing MTP based on resampling [Dudoit, van der Laan 2008]. A wide range of applications, the possibility of choosing the Type I error rate and easily accessible software (MTP procedure is implemented in R multtest package) are their obvious advantages. Unfortunately, the results of the analysis of the MTP procedure obtained by Werft and Benner [2009] revealed problems with controlling FDR in the case of numerous sets of hypotheses and small samples. The paper presents a simulation experiment conducted to investigate potential restrictions of MTP procedure in case of large numbers of inferences and large sample sizes, which is typical of Big Data analyses. The experiment revealed that, regardless of the sample size, problems with controlling FDR occur when multiple testing procedures based on minima of unadjusted p-values ( ) are applied. Moreover, the experiment indicated the serious instability of the results of the MTP procedure (dependent on the number of bootstrap samplings) if multiple testing procedures based on minima of unadjusted p-values ( ) are used. The experiment described in the paper and the results obtained by Werft, Benner [2009] and Denkowska [2013] indicate the need for further research on MTP procedure.
2
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The modification of stepwise multiple procedure

100%
Parys D., University of Łódź C. o. S. M.
Acta Universitatis Lodziensis. Folia Oeconomica
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2008
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vol. 216
EN
In this paper we discuss stepdown methods that control the familywise error rate in finite samples. Such methods proceed stagewise by testing an intersection hypothesis without regard to hypotheses previously rejected. However, one cannot always achieve strong control in such a simple manner. By understanding the limitations of this approach in finite samples, we can then see why an asymptotic approach will be valid under fairly weak assumptions. It turns out that a simple monotonicity condition for theoretical critical values allows for some immediate results.
PL
Procedury kroczące w porównaniach wielokrotnych często nie są w stanie zachować silnej kontroli nad błędem rodziny (tzw. familywise errors rate FWE). Prezentujemy tutaj ogólną metodę wnioskowania wielokrotnego opartego na krokach zstępujących i na jej tle proponujemy metodę wykorzystując modyfikację stałych krytycznych, które lepiej sprawują kontrolę nad FWE dla prób skończonych.
3
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Testowanie wielokrotne w badaniach ekonomicznych

75%
Denkowska S.
Folia Oeconomica Cracoviensia
|
2007
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vol. 48
119-135
EN
In the paper multiple testing procedures based on ordered p-values are applied to control type I errors rates for family of inferences in different statistical problems. Multiple testing procedures based on ordered p-values may be found an interesting tool for simultaneous testing of more than one hypothesis at a time. Discussed methods are applicable to a broad spectrum of statistical problems since their requirements for statistical assumption are considerably less restricted than in case of classical procedures (only dependency among test statistics should be controlled). The analysis is put down to a collection of p-values or adjusted p-values. Depending on approach to the control of Type I error for the family of inferences these methods may be categorized into two major groups: FWE (Family-Wise Error Rate) and FDR (False Discovery Rate) procedures. The procedures of multiple testing are applied to typical situations in economics research: to separate homogenous groups of means, to test the significance of correlation coefficients in the correlation matrix and to infer about significance of regression parameters in linear regression model.
4
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Nieklasyczne procedury testowań wielokrotnych

63%
Denkowska S.
Przegląd Statystyczny
|
2013
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vol. 60
|
issue 4
461-476
PL
Zakres zastosowań klasycznych procedur testowań wielokrotnych jest ograniczony z powodu założeń modelowych, a w wielu sytuacjach badawczych rozwiązań klasycznych po prostu brak. Kontrolę efektu testowania wielokrotnego umożliwiają wówczas nieklasyczne procedury testowań wielokrotnych. Proste obliczeniowo, o szerokim zakresie zastosowań, brzegowe procedury testowań wielokrotnych nie uwzględniają jednak łącznego rozkładu statystyk testowych, przez co są bardziej konserwatywne od procedur łącznych. Zakres zastosowań procedur łącznych Westfalla i Younga (1993) jest natomiast ograniczony ze względu na wymóg obrotowości podzbioru. Ciekawą alternatywę stanowią dedykowane badaniom genetycznym procedury łączne, zaproponowane przez Dudoit oraz van der Laana (2008). Szeroki zakres zastosowań, możliwość wyboru miary błędu I rodzaju oraz powszechnie dostępne, oprogramowanie (procedura MTP jest zaimplementowana w pakiecie multtest w R), to ich istotne zalety. Niestety, badania nad procedurą MTP przeprowadzone przez Werfta i Bennera (2009) pokazały problemy z kontrolą miary FDR w przypadku bardzo dużej liczby testowanych hipotez i małej liczebności prób. Z kolei zaprezentowany w artykule eksperyment symulacyjny pokazał, że procedura MTP nie zapewnia również kontroli FWER na z góry zadanym poziomie.
EN
The range of applications of classical multiple testing procedures is limited due to model assumptions, and in many cases classic solutions are non-existent. In such situations non-classical multiple testing procedures allow to control the effect of multiple testing. Although they are popular for computational simplicity and a wide range of applications, marginal multiple testing procedures do not take into account joint distribution of test statistics, which make them more conservative than joint multiple testing procedures. The range of applications of joint procedures introduced by Westfall and Young (1993) is limited due to the subset pivotality requirement. Thus, joint multiple testing procedures suggested by Dudoit and van der Laan (2008) seem very promising. A wide range of applications, the possibility of choosing the Type I error rate and easily accessible software (MTP procedure is implemented in R multtest package) are their obvious advantages. Unfortunately, the results of the analysis of MPT procedure obtained by Werft and Benner (2009) revealed that it does not control FDR in case of numerous sets of hypotheses and small samples. Furthermore, the simulation experiment presented in the article showed that MTP procedure does not control FWER, either.
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