Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userNon-parametric Archimedean generator estimation with implications for multiple testing
75
0
0.0
(
0
)
Added by
Thorsten Dickhaus
Publication date
2019
fields
Mathematical Statistics
and research's language is
English
Ask ChatGPT about the research
No Arabic abstract
In multiple testing, the family-wise error rate can be bounded under some conditions by the copula of the test statistics. Assuming that this copula is Archimedean, we consider two non-parametric Archimedean generator estimators. More specifically, we use the non-parametric estimator from Genest et al. (2011) and a slight modification thereof. In simulations, we compare the resulting multiple tests with the Bonferroni test and the multiple test derived from the true generator as baselines.
rate research
Read More
Non-parametric maximum likelihood estimation encompasses a group of classic methods to estimate distribution-associated functions from potentially censored and truncated data, with extensive applications in survival analysis. These methods, including the Kaplan-Meier estimator and Turnbulls method, often result in overfitting, especially when the sample size is small. We propose an improvement to these methods by applying kernel smoothing to their raw estimates, based on a BIC-type loss function that balances the trade-off between optimizing model fit and controlling model complexity. In the context of a longitudinal study with repeated observations, we detail our proposed smoothing procedure and optimization algorithm. With extensive simulation studies over multiple realistic scenarios, we demonstrate that our smoothing-based procedure provides better overall accuracy in both survival function estimation and individual-level time-to-event prediction by reducing overfitting. Our smoothing procedure decreases the discrepancy between the estimated and true simulated survival function using interval-censored data by up to 49% compared to the raw un-smoothed estimate, with similar improvements of up to 41% and 23% in within-sample and out-of-sample prediction, respectively. Finally, we apply our method to real data on censored breast cancer diagnosis, which similarly shows improvement when compared to empirical survival estimates from uncensored data. We provide an R package, SISE, for implementing our penalized likelihood method.
Non-parametric goodness-of-fit testing procedures based on kernel Stein discrepancies (KSD) are promising approaches to validate general unnormalised distributions in various scenarios. Existing works have focused on studying optimal kernel choices to boost test performances. However, the Stein operators are generally non-unique, while different choices of Stein operators can also have considerable effect on the test performances. In this work, we propose a unifying framework, the generalised kernel Stein discrepancy (GKSD), to theoretically compare and interpret different Stein operators in performing the KSD-based goodness-of-fit tests. We derive explicitly that how the proposed GKSD framework generalises existing Stein operators and their corresponding tests. In addition, we show thatGKSD framework can be used as a guide to develop kernel-based non-parametric goodness-of-fit tests for complex new data scenarios, e.g. truncated distributions or compositional data. Experimental results demonstrate that the proposed tests control type-I error well and achieve higher test power than existing approaches, including the test based on maximum-mean-discrepancy (MMD).
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 algorithmic 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.
Hierarchical inference in (generalized) regression problems is powerful for finding significant groups or even single covariates, especially in high-dimensional settings where identifiability of the entire regression parameter vector may be ill-posed. The general method proceeds in a fully data-driven and adaptive way from large to small groups or singletons of covariates, depending on the signal strength and the correlation structure of the design matrix. We propose a novel hierarchical multiple testing adjustment that can be used in combination with any significance test for a group of covariates to perform hierarchical inference. Our adjustment passes on the significance level of certain hypotheses that could not be rejected and is shown to guarantee strong control of the familywise error rate. Our method is at least as powerful as a so-called depth-wise hierarchical Bonferroni adjustment. It provides a substantial gain in power over other previously proposed inheritance hierarchical procedures if the underlying alternative hypotheses occur sparsely along a few branches in the tree-structured hierarchy.
Multiple testing problems are a staple of modern statistical analysis. The fundamental objective of multiple testing procedures is to reject as many false null hypotheses as possible (that is, maximize some notion of power), subject to controlling an overall measure of false discovery, like family-wise error rate (FWER) or false discovery rate (FDR). In this paper we formulate multiple testing of simple hypotheses as an infinite-dimensional optimization problem, seeking the most powerful rejection policy which guarantees strong control of the selected measure. In that sense, our approach is a generalization of the optimal Neyman-Pearson test for a single hypothesis. We show that for exchangeable hypotheses, for both FWER and FDR and relevant notions of power, these problems can be formulated as infinite linear programs and can in principle be solved for any number of hypotheses. We also characterize maximin rules for complex alternatives, and demonstrate that such rules can be found in practice, leading to improved practical procedures compared to existing alternatives. We derive explicit optimal tests for FWER or FDR control for three independent normal means. We find that the power gain over natural competitors is substantial in all settings examined. Finally, we apply our optimal maximin rule to subgroup analyses in systematic reviews from the Cochrane library, leading to an increase in the number of findings while guaranteeing strong FWER control against the one sided alternative.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
