109 research outputs found
Self-concordant profile empirical likelihood ratio tests for the population correlation coefficient: A simulation study
We present results of a simulation study regarding the finite-sample type I error behavior of the self-concordant profile empirical likelihood ratio (ELR) test for the population correlation coefficient. Three different families of bivariate elliptical distributions are taken into account. Uniformly over all considered models and parameter configurations, the self-concordant profile ELR test does not keep the significance level for finite sample sizes, albeit the level exceedance monotonously decreases to zero as the sample size increases. We discuss some potential modifications to address this problem
Simultaneous Bayesian analysis of contingency tables in genetic association studies
Genetic association studies lead to simultaneous categorical data analysis. The sample for every genetic locus consists of a contingency table containing the numbers of observed genotype-phenotype combinations. Under case-control design, the row counts of every table are identical and fixed, while column counts are random. The aim of the statistical analysis is to test independence of the phenotype and the genotype at every locus. We present an objective Bayesian methodology for these association tests, utilizing the Bayes factor proposed by Good (1976) and Crook and Good (1980). It relies on the conjugacy of Dirichlet and multinomial distributions, where the hyperprior for the Dirichlet parameter is log-Cauchy. Being based on the likelihood principle, the Bayesian tests avoid looping over all tables with given marginals. Hence, their computational burden does not increase with the sample size, in contrast to frequentist exact tests. Making use of data generated by The Wellcome Trust Case Control Consortium (2007), we illustrate that the ordering of the Bayes factors shows a good agreement with that of frequentist p-values. Furthermore, we deal with specifying prior probabilities for the validity of the null hypotheses, by taking linkage disequilibrium structure into account and exploiting the concept of effective numbers of tests. Application of a Bayesian decision theoretic multiple test procedure to The Wellcome Trust Case Control Consortium (2007) data illustrates the proposed methodology. Finally, we discuss two methods for reconciling frequentist and Bayesian approaches to the multiple association test problem for contingency tables in genetic association studies
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Self-concordant profile empirical likelihood ratio tests for the population correlation coefficient: A simulation study
We present results of a simulation study regarding the finite-sample
type I error behavior of the self-concordant profile empirical likelihood
ratio (ELR) test for the population correlation coefficient. Three different
families of bivariate elliptical distributions are taken into account.
Uniformly over all considered models and parameter configurations, the
self-concordant profile ELR test does not keep the significance level for
finite sample sizes, albeit the level exceedance monotonously decreases to
zero as the sample size increases. We discuss some potential modifications to
address this problem
On the false discovery rate and an asymptotically optimal rejection curve
In this paper we introduce and investigate a new rejection curve for
asymptotic control of the false discovery rate (FDR) in multiple hypotheses
testing problems. We first give a heuristic motivation for this new curve and
propose some procedures related to it. Then we introduce a set of possible
assumptions and give a unifying short proof of FDR control for procedures based
on Simes' critical values, whereby certain types of dependency are allowed.
This methodology of proof is then applied to other fixed rejection curves
including the proposed new curve. Among others, we investigate the problem of
finding least favorable parameter configurations such that the FDR becomes
largest. We then derive a series of results concerning asymptotic FDR control
for procedures based on the new curve and discuss several example procedures in
more detail. A main result will be an asymptotic optimality statement for
various procedures based on the new curve in the class of fixed rejection
curves. Finally, we briefly discuss strict FDR control for a finite number of
hypotheses.Comment: Published in at http://dx.doi.org/10.1214/07-AOS569 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Dependency and false discovery rate: Asymptotics
Some effort has been undertaken over the last decade to provide conditions
for the control of the false discovery rate by the linear step-up procedure
(LSU) for testing hypotheses when test statistics are dependent. In this
paper we investigate the expected error rate (EER) and the false discovery rate
(FDR) in some extreme parameter configurations when tends to infinity for
test statistics being exchangeable under null hypotheses. All results are
derived in terms of -values. In a general setup we present a series of
results concerning the interrelation of Simes' rejection curve and the
(limiting) empirical distribution function of the -values. Main objects
under investigation are largest (limiting) crossing points between these
functions, which play a key role in deriving explicit formulas for EER and FDR.
As specific examples we investigate equi-correlated normal and -variables in
more detail and compute the limiting EER and FDR theoretically and numerically.
A surprising limit behavior occurs if these models tend to independence.Comment: Published in at http://dx.doi.org/10.1214/009053607000000046 the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
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On multivariate chi-square distributions and their applications in testing multiple hypotheses
We are considered with three different types of multivariate chi-square
distributions. Their members play important roles as limiting distributions
of vectors of test statistics in several applications of multiple hypotheses
testing. We explain these applications and provide formulas for computing
multiplicity-adjusted p-values under the respective global hypothesis
On multivariate chi-square distributions and their applications in testing multiple hypotheses
We are considered with three different types of multivariate chi-square distributions. Their members play important roles as limiting distributions of vectors of test statistics in several applications of multiple hypotheses testing. We explain these applications and provide formulas for computing multiplicity-adjusted -values under the respective global hypothesis
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