اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدHeterocedasticity-Adjusted Ranking and Thresholding for Large-Scale Multiple Testing
111
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
Standardization has been a widely adopted practice in multiple testing, for it takes into account the variability in sampling and makes the test statistics comparable across different study units. However, despite conventional wisdom to the contrary, we show that there can be a significant loss in information from basing hypothesis tests on standardized statistics rather than the full data. We develop a new class of heteroscedasticity--adjusted ranking and thresholding (HART) rules that aim to improve existing methods by simultaneously exploiting commonalities and adjusting heterogeneities among the study units. The main idea of HART is to bypass standardization by directly incorporating both the summary statistic and its variance into the testing procedure. A key message is that the variance structure of the alternative distribution, which is subsumed under standardized statistics, is highly informative and can be exploited to achieve higher power. The proposed HART procedure is shown to be asymptotically valid and optimal for false discovery rate (FDR) control. Our simulation results demonstrate that HART achieves substantial power gain over existing methods at the same FDR level. We illustrate the implementation through a microarray analysis of myeloma.
قيم البحث
اقرأ أيضاً
This paper investigates the high-dimensional linear regression with highly correlated covariates. In this setup, the traditional sparsity assumption on the regression coefficients often fails to hold, and consequently many model selection procedures
do not work. To address this challenge, we model the variations of covariates by a factor structure. Specifically, strong correlations among covariates are explained by common factors and the remaining variations are interpreted as idiosyncratic components of each covariate. This leads to a factor-adjusted regression model with both common factors and idiosyncratic components as covariates. We generalize the traditional sparsity assumption accordingly and assume that all common factors but only a small number of idiosyncratic components contribute to the response. A Bayesian procedure with a spike-and-slab prior is then proposed for parameter estimation and model selection. Simulation studies show that our Bayesian method outperforms its lasso analogue, manifests insensitivity to the overestimates of the number of common factors, pays a negligible price in the no correlation case, and scales up well with increasing sample size, dimensionality and sparsity. Numerical results on a real dataset of U.S. bond risk premia and macroeconomic indicators lend strong support to our methodology.
We propose a new adaptive empirical Bayes framework, the Bag-Of-Null-Statistics (BONuS) procedure, for multiple testing where each hypothesis testing problem is itself multivariate or nonparametric. BONuS is an adaptive and interactive knockoff-type
method that helps improve the testing power while controlling the false discovery rate (FDR), and is closely connected to the counting knockoffs procedure analyzed in Weinstein et al. (2017). Contrary to procedures that start with a $p$-value for each hypothesis, our method analyzes the entire data set to adaptively estimate an optimal $p$-value transform based on an empirical Bayes model. Despite the extra adaptivity, our method controls FDR in finite samples even if the empirical Bayes model is incorrect or the estimation is poor. An extension, the Double BONuS procedure, validates the empirical Bayes model to guard against power loss due to model misspecification.
In this article, motivated by biosurveillance and censoring sensor networks, we investigate the problem of distributed monitoring large-scale data streams where an undesired event may occur at some unknown time and affect only a few unknown data stre
ams. We propose to develop scalable global monitoring schemes by parallel running local detection procedures and by combining these local procedures together to make a global decision based on SUM-shrinkage techniques. Our approach is illustrated in two concrete examples: one is the nonhomogeneous case when the pre-change and post-change local distributions are given, and the other is the homogeneous case of monitoring a large number of independent $N(0,1)$ data streams where the means of some data streams might shift to unknown positive or negative values. Numerical simulation studies demonstrate the usefulness of the proposed schemes.
We derive new algorithms for online multiple testing that provably control false discovery exceedance (FDX) while achieving orders of magnitude more power than previous methods. This statistical advance is enabled by the development of new algorithmi
c ideas: earlier algorithms are more static while our new ones allow for the dynamical adjustment of testing levels based on the amount of wealth the algorithm has accumulated. We demonstrate that our algorithms achieve higher power in a variety of synthetic experiments. We also prove that SupLORD can provide error control for both FDR and FDX, and controls FDR at stopping times. Stopping times are particularly important as they permit the experimenter to end the experiment arbitrarily early while maintaining desired control of the FDR. SupLORD is the first non-trivial algorithm, to our knowledge, that can control FDR at stopping times in the online setting.
A central goal in designing clinical trials is to find the test that maximizes power (or equivalently minimizes required sample size) for finding a true research hypothesis subject to the constraint of type I error. When there is more than one test,
such as in clinical trials with multiple endpoints, the issues of optimal design and optimal policies become more complex. In this paper we address the question of how such optimal tests should be defined and how they can be found. We review different notions of power and how they relate to study goals, and also consider the requirements of type I error control and the nature of the policies. This leads us to formulate the optimal policy problem as an explicit optimization problem with objective and constraints which describe its specific desiderata. We describe a complete solution for deriving optimal policies for two hypotheses, which have desired monotonicity properties, and are computationally simple. For some of the optimization formulations this yields optimal policies that are identical to existing policies, such as Hommels procedure or the procedure of Bittman et al. (2009), while for others it yields completely novel and more powerful policies than existing ones. We demonstrate the nature of our novel policies and their improved power extensively in simulation and on the APEX study (Cohen et al., 2016).
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
