单调趋势的置换检验

Optimal Rates of Statistical Seriation

Given a matrix the seriation problem consists in permuting its rows in such way that all its columns have the same shape, for example, they are monotone increasing. We propose a statistical approach to this problem where the matrix of interest is observed with noise and study the corresponding minimax rate of estimation of the matrices. Specifically, when the columns are either unimodal or monotone, we show that the least squares estimator is optimal up to logarithmic factors and adapts to matrices with a certain natural structure. Finally, we propose a computationally efficient estimator in t…

Permuted and Unlinked Monotone Regression in $\mathbb{R}^d$: an approach based on mixture modeling and optimal transport

Suppose that we have a regression problem with response variable Y in $\mathbb{R}^d$ and predictor X in $\mathbb{R}^d$, for $d \geq 1$. In permuted or unlinked regression we have access to separate unordered data on X and Y, as opposed to data on (X,Y)-pairs in usual regression. So far in the literature the case $d=1$ has received attention, see e.g., the recent papers by Rigollet and Weed [Information & Inference, 8, 619--717] and Balabdaoui et al. [J. Mach. Learn. Res., 22(172), 1--60]. In this paper, we consider the general multivariate setting with $d \geq 1$. We show that the notion of cy…

ProgPermute: Progressive permutation for a dynamic representation of the robustness of microbiome discoveries

Identification of features is a critical task in microbiome studies that is complicated by the fact that microbial data are high dimensional and heterogeneous. Masked by the complexity of the data, the problem of separating signals from noise becomes challenging and troublesome. For instance, when performing differential abundance tests, multiple testing adjustments tend to be overconservative, as the probability of a type I error (false positive) increases dramatically with the large numbers of hypotheses. Moreover, the grouping effect of interest can be obscured by heterogeneity. These facto…

时间序列中基于最小二乘的置换检验

Least Squares-Based Permutation Tests in Time Series

本文针对平稳弱依赖时间序列的回归参数与无单调趋势问题，构造了渐近有效且可交换性成立时仍精确的置换检验方法，并公开了R包permixOLS供使用。

Analyzing Ozone Concentration by Bayesian Spatio-temporal Quantile Regression

Ground level Ozone is one of the six common air-pollutants on which the EPA has set national air quality standards. In order to capture the spatio-temporal trend of 1-hour and 8-hour average ozone concentration in the US, we develop a method for spatio-temporal simultaneous quantile regression. Unlike existing procedures, in the proposed method, smoothing across the sites is incorporated within modeling assumptions thus allowing borrowing of information across locations, an essential step when the number of samples in each location is low. The quantile function has been assumed to be linear in…

BOSS -- 生物标志物最优分割系统

BOSS -- Biomarker Optimal Segmentation System

BOSS方法通过高效计算实现连续生物标志物最优截断值的快速搜索与检验，在保持统计功效和错误控制的同时，比置换方法快数百倍，并应用于肺腺癌数据发现潜在趋同生物标志物。

极端情况下的假设检验：高通量数据的快速和稳健关联

Hypothesis testing at the extremes: fast and robust association for high-throughput data

许多生物医学问题需要进行许多假设检验，并随之需要应用严格的阈值。数据通常采用一系列预测向量的形式，每个预测向量都必须与单个响应向量进行比较，可能还有干扰协变量。关联的参数检验经常使用，但在极端阈值下可能导致不准确的第一类错误，即使是大样本量。此外，由于零分布的不对称性，与加倍的$p$值相比，标准双侧检验可能降低功效。精确（置换）测试是有吸引力的，但可能是计算密集型和繁琐的。我们提出了一个近似的趋势，是准确和快速的标准使用在高通量设置，并可以很容易地提供标准的双侧或双$p$值的精确关联测试。最常用的广义线性模型的排列下的似然比检验的方法是等效的。对于线性回归，通过处理协变量残差化响应和预测变量来处理协变量。对于广义线性模型，分层协变量的处理方式类似于精确条件检验。仿真和实例说明了该方法的广泛适用性。

A test against trend in random sequences

We study a modification of Kendall's tau-test, replacing his permutations of n different numbers by sequences of length n, where repetition is allowed. In particular, binary sequences are included. Random sequences can be tested.

Should We Adjust for the Test for Pre-trends in Difference-in-Difference Designs?

The common practice in difference-in-difference (DiD) designs is to check for parallel trends prior to treatment assignment, yet typical estimation and inference does not account for the fact that this test has occurred. I analyze the properties of the traditional DiD estimator conditional on having passed (i.e. not rejected) the test for parallel pre-trends. When the DiD design is valid and the test for pre-trends confirms it, the typical DiD estimator is unbiased, but traditional standard errors are overly conservative. Additionally, there exists an alternative unbiased estimator that is mor…

Some New Copula Based Distribution-free Tests of Independence among Several Random Variables

Over the last couple of decades, several copula based methods have been proposed in the literature to test for the independence among several random variables. But these existing tests are not invariant under monotone transformations of the variables, and they often perform poorly if the dependence among the variables is highly non-monotone in nature. In this article, we propose a copula based measure of dependency and use it to construct some new distribution-free tests of independence. The proposed measure and the resulting tests, all are invariant under permutations and monotone transformat…

High dimensional consistent independence testing with maxima of rank correlations

Testing mutual independence for high-dimensional observations is a fundamental statistical challenge. Popular tests based on linear and simple rank correlations are known to be incapable of detecting non-linear, non-monotone relationships, calling for methods that can account for such dependences. To address this challenge, we propose a family of tests that are constructed using maxima of pairwise rank correlations that permit consistent assessment of pairwise independence. Built upon a newly developed Cramér-type moderate deviation theorem for degenerate U-statistics, our results cover a vari…