Related papers: Moment based gene set tests
We consider the problem of testing whether a single coefficient is equal to zero in linear models when the dimension of covariates $p$ can be up to a constant fraction of sample size $n$. In this regime, an important topic is to propose…
We introduce the notion of a weighted inversion statistic on the symmetric group, and examine its distribution on each conjugacy class. Our work generalizes the study of several common permutation statistics, including the number of…
We study sorting of permutations by random swaps if each comparison gives the wrong result with some fixed probability $p<1/2$. We use this process as prototype for the behaviour of randomized, comparison-based optimization heuristics in…
It is imperative for testing to determine if the components within large-scale software systems operate functionally. Interaction testing involves designing a suite of tests, which guarantees to detect a fault if one exists among a small…
When primed with only a handful of training samples, very large, pretrained language models such as GPT-3 have shown competitive results when compared to fully-supervised, fine-tuned, large, pretrained language models. We demonstrate that…
Variable selection in high-dimensional scenarios is of great interested in statistics. One application involves identifying differentially expressed genes in genomic analysis. Existing methods for addressing this problem have some limits or…
Testing for change points in sequences of covariance matrices is an important and equally challenging problem in statistical methodology with applications in various fields. Motivated by the observation that even in cases where the ratio…
Recent advances in genotyping technology have delivered a wealth of genetic data, which is rapidly advancing our understanding of the underlying genetic architecture of complex diseases. Mendelian Randomization (MR) leverages such genetic…
It is numerically well known that moment-based tests for Gaussianity and estimators become increasingly unreliable at higher moment orders; however, this phenomenon has lacked rigorous mathematical justification. In this work, we establish…
Various statistical tests have been developed for testing the equality of means in matched pairs with missing values. However, most existing methods are commonly based on certain distributional assumptions such as normality, 0-symmetry or…
The topic of the article is the parametric study of the complexity of algorithms on arrays of pairwise distinct integers. We introduce a model that takes into account the non-uniformness of data, which we call the Ewens-like distribution of…
Counting distinct permutations with replacement, especially when involving multiple subwords, is a longstanding challenge in combinatorial analysis, with critical applications in cryptography, bioinformatics, and statistical modeling. This…
Matching is an appealing way to design observational studies because it mimics the data structure produced by stratified randomized trials, pairing treated individuals with similar controls. After matching, inference is often conducted…
Researchers in data-rich disciplines---think of computational genomics and observational cosmology---often wish to mine large bodies of $p$-values looking for significant effects, while controlling the false discovery rate or family-wise…
We propose a kernel-based partial permutation test for checking the equality of functional relationship between response and covariates among different groups. The main idea, which is intuitive and easy to implement, is to keep the…
Beginning with work of Zeilberger on classical pattern counts, there are a variety of structural results for moments of permutation statistics applied to random permutations. Using tools from representation theory, Gaetz and Ryba…
In this paper, we develop an explicit formula allowing to compute the first k moments of the random count of a pattern in a multi-states sequence generated by a Markov source. We derive efficient algorithms allowing to deal both with low or…
Increasing accessibility of data to researchers makes it possible to conduct massive amounts of statistical testing. Rather than follow a carefully crafted set of scientific hypotheses with statistical analysis, researchers can now test…
The goal of property testing is to quickly distinguish between objects which satisfy a property and objects that are $\epsilon$-far from satisfying the property. There are now several general results in this area which show that natural…
Historically, the majority of statistical association methods have been designed assuming availability of SNP-level information. However, modern genetic and sequencing data present new challenges to access and sharing of genotype-phenotype…