arXiv subjects

Joshua D. Habiger

Publications and source records attributed to Joshua D. Habiger.

5 recordsLinked to original sources

arXiv2017

The Inuence of Misspecified Covariance on False Discovery Control when Using Posterior Probabilities

This paper focuses on the influence of a misspecified covariance structure on false discovery rate for the large scale multiple testing problem. Specifically, we evaluate the influence on the marginal distribution of local fdr statistics, which are used in many multiple testing procedures and related to Bayesian posterior probabilities. Explicit forms of the marginal distributions under both correctly specified and incorrectly specified models are derived. The Kullback-Leibler divergence is used to quantify the influence caused by a misspecification. Several numerical examples are provided to illustrate the influence. A real spatio-temporal data on soil humidity is discussed.

math.ST↗

arXiv2017

Adaptive False Discovery Rate Control for Heterogeneous Data

Efforts to develop more efficient multiple hypothesis testing procedures for false discovery rate (FDR) control have focused on incorporating an estimate of the proportion of true null hypotheses (such procedures are called adaptive) or exploiting heterogeneity across tests via some optimal weighting scheme. This paper combines these approaches using a weighted adaptive multiple decision function (WAMDF) framework. Optimal weights for a flexible random effects model are derived and a WAMDF that controls the FDR for arbitrary weighting schemes when test statistics are independent under the null hypotheses is given. Asymptotic and numerical assessment reveals that, under weak dependence, the proposed WAMDFs provide more efficient FDR control even if optimal weights are misspecified. The robustness and flexibility of the proposed methodology facilitates the development of more efficient, yet practical, FDR procedures for heterogeneous data. To illustrate, two different weighted adaptive FDR methods for heterogeneous sample sizes are developed and applied to data.

stat.ME↗

arXiv2011

Compound p-Value Statistics for Multiple Testing Procedures

Many multiple testing procedures make use of the p-values from the individual pairs of hypothesis tests, and are valid if the p-value statistics are independent and uniformly distributed under the null hypotheses. However, it has recently been shown that these types of multiple testing procedures are inefficient since such p-values do not depend upon all of the available data. This paper provides tools for constructing compound p-value statistics, which are those that depend upon all of the available data, but still satisfy the conditions of independence and uniformity under the null hypotheses. As an example, a class of compound p-value statistics for testing for location shifts is developed. It is demonstrated, both analytically and through simulations, that multiple testing procedures tend to reject more false null hypotheses when applied to these compound p-values rather than the usual p-values, and at the same time still guarantee the desired type I error rate control. The compound p-values, in conjunction with two different multiple testing methods, are used to analyze a real microarray data set. Applying either multiple testing method to the compound p-values, instead of the usual p-values, enhances their powers.

stat.ME↗

arXiv2011

Power-enhanced multiple decision functions controlling family-wise error and false discovery rates

Improved procedures, in terms of smaller missed discovery rates (MDR), for performing multiple hypotheses testing with weak and strong control of the family-wise error rate (FWER) or the false discovery rate (FDR) are developed and studied. The improvement over existing procedures such as the Šidák procedure for FWER control and the Benjamini--Hochberg (BH) procedure for FDR control is achieved by exploiting possible differences in the powers of the individual tests. Results signal the need to take into account the powers of the individual tests and to have multiple hypotheses decision functions which are not limited to simply using the individual $p$-values, as is the case, for example, with the Šidák, Bonferroni, or BH procedures. They also enhance understanding of the role of the powers of individual tests, or more precisely the receiver operating characteristic (ROC) functions of decision processes, in the search for better multiple hypotheses testing procedures. A decision-theoretic framework is utilized, and through auxiliary randomizers the procedures could be used with discrete or mixed-type data or with rank-based nonparametric tests. This is in contrast to existing $p$-value based procedures whose theoretical validity is contingent on each of these $p$-value statistics being stochastically equal to or greater than a standard uniform variable under the null hypothesis. Proposed procedures are relevant in the analysis of high-dimensional "large $M$, small $n$" data sets arising in the natural, physical, medical, economic and social sciences, whose generation and creation is accelerated by advances in high-throughput technology, notably, but not limited to, microarray technology.

math.ST↗

arXiv2010

Classes of Multiple Decision Functions Strongly Controlling FWER and FDR

This paper provides two general classes of multiple decision functions where each member of the first class strongly controls the family-wise error rate (FWER), while each member of the second class strongly controls the false discovery rate (FDR). These classes offer the possibility that an optimal multiple decision function with respect to a pre-specified criterion, such as the missed discovery rate (MDR), could be found within these classes. Such multiple decision functions can be utilized in multiple testing, specifically, but not limited to, the analysis of high-dimensional microarray data sets.

math.ST↗