scholarly journals Multiple testing with discrete data: Proportion of true null hypotheses and two adaptive FDR procedures

2018 ◽  
Vol 60 (4) ◽  
pp. 761-779 ◽  
Author(s):  
Xiongzhi Chen ◽  
Rebecca W. Doerge ◽  
Joseph F. Heyse
Keyword(s):  
Multiple Testing ◽  
Discrete Data ◽  
True Null Hypotheses

An extended sequential goodness-of-fit multiple testing method for discrete data

2015 ◽  
Vol 26 (5) ◽  
pp. 2356-2375 ◽  
Author(s):  
Irene Castro-Conde ◽  
Sebastian Döhler ◽  
Jacobo de Uña-Álvarez
Keyword(s):  
Multiple Testing ◽  
Goodness Of Fit ◽  
Discrete Data ◽  
Testing Method

scholarly journals Estimating the Proportion of True Null Hypotheses in Multiple Testing Problems

2016 ◽  
Vol 2016 ◽  
pp. 1-7
Author(s):  
Oluyemi Oyeniran ◽  
Hanfeng Chen
Keyword(s):  
Multiple Testing ◽  
Large Scale ◽  
Simulation Studies ◽  
Multinomial Models ◽  
Nonparametric Likelihood ◽  
False Discovery ◽  
Likelihood Approach ◽  
Multiple Testing Problem ◽  
True Null Hypotheses ◽  
Microarray Datasets

The problem of estimating the proportion, π0, of the true null hypotheses in a multiple testing problem is important in cases where large scale parallel hypotheses tests are performed independently. While the problem is a quantity of interest in its own right in applications, the estimate of π0 can be used for assessing or controlling an overall false discovery rate. In this article, we develop an innovative nonparametric maximum likelihood approach to estimate π0. The nonparametric likelihood is proposed to be restricted to multinomial models and an EM algorithm is also developed to approximate the estimate of π0. Simulation studies show that the proposed method outperforms other existing methods. Using experimental microarray datasets, we demonstrate that the new method provides satisfactory estimate in practice.

scholarly journals Biostatistics for Multiple Testing

2020 ◽  
Vol 63 (3) ◽  
pp. 97-100
Author(s):  
Jeong-Seok Choi
Keyword(s):  
False Discovery Rate ◽  
Error Rate ◽  
Null Hypothesis ◽  
Multiple Testing ◽  
Statistical Techniques ◽  
Testing Hypotheses ◽  
Family Wise Error Rate ◽  
False Discovery ◽  
The Family ◽  
True Null Hypotheses

Multiple testings are instances that contain simultaneous tests for more than one hypothesis. When multiple testings are conducted at the same time, it is more likely that the null hypothesis is rejected, even if the null hypothesis is correct. If individual hypothesis decisions are based on unadjusted <i>p</i>-values, it is usually more likely that some of the true null hypotheses will be rejected. In order to solve the multiple testing problems, various studies have attempted to increase the power by taking into account the family-wise error rate or false discovery rate and statistics required for testing hypotheses. This article discuss methods that account for the multiplicity issue and introduces various statistical techniques.

Integrated Fractional white Noise as an Alternative to Multifractional Brownian Motion

2007 ◽  
Vol 44 (02) ◽  
pp. 393-408 ◽  
Author(s):  
Allan Sly
Keyword(s):  
Stochastic Process ◽  
Brownian Motion ◽  
White Noise ◽  
Gaussian Process ◽  
Discrete Data ◽  
Hölder Exponent ◽  
Scaling Properties ◽  
Multifractional Brownian Motion ◽  
Local Properties

Multifractional Brownian motion is a Gaussian process which has changing scaling properties generated by varying the local Hölder exponent. We show that multifractional Brownian motion is very sensitive to changes in the selected Hölder exponent and has extreme changes in magnitude. We suggest an alternative stochastic process, called integrated fractional white noise, which retains the important local properties but avoids the undesirable oscillations in magnitude. We also show how the Hölder exponent can be estimated locally from discrete data in this model.

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