Related papers: Testing Independence under Biased Sampling

The two-sample problem, which consists in testing whether independent samples on $\mathbb{R}^d$ are drawn from the same (unknown) distribution, finds applications in many areas. Its study in high-dimension is the subject of much attention,…

Testing independence is of significant interest in many important areas of large-scale inference. Using extreme-value form statistics to test against sparse alternatives and using quadratic form statistics to test against dense alternatives…

Truncation is a statistical phenomenon that occurs in many time to event studies. For example, autopsy-confirmed studies of neurodegenerative diseases are subject to an inherent left and right truncation, also known as double truncation.…

Measuring dependence between random variables is a fundamental problem in Statistics, with applications across diverse fields. While classical measures such as Pearson's correlation have been widely used for over a century, they have…

A number of biomedical problems require performing many hypothesis tests, with an attendant need to apply stringent thresholds. Often the data take the form of a series of predictor vectors, each of which must be compared with a single…

It is a common saying that testing for conditional independence, i.e., testing whether whether two random vectors $X$ and $Y$ are independent, given $Z$, is a hard statistical problem if $Z$ is a continuous random variable (or vector). In…

We consider the following problem: given the weights of two models, can we test whether they were trained independently -- i.e., from independent random initializations? We consider two settings: constrained and unconstrained. In the…

This paper takes a different look on the problem of testing the mutual independence of the components of a high-dimensional vector. Instead of testing if all pairwise associations (e.g. all pairwise Kendall's $\tau$) between the components…

We formulate nonparametric and semiparametric hypothesis testing of multivariate stationary linear time series in a unified fashion and propose new test statistics based on estimators of the spectral density matrix. The limiting…

Testing conditional independence has many applications, such as in Bayesian network learning and causal discovery. Different test methods have been proposed. However, existing methods generally can not work when only discretized…

We provide a unified framework for independence and mean independence tests based on the Hilbert-Schmidt independence criterion, extending some previous results in the literature to hold in general topological spaces. We also present a…

In this paper new tests for the independence of two high-dimensional vectors are investigated. We consider the case where the dimension of the vectors increases with the sample size and propose multivariate analysis of variance-type…

Copulas are mathematical objects that fully capture the dependence structure among random variables and hence, offer a great flexibility in building multivariate stochastic models. In statistics, a copula is used as a general way of…

Permutation tests are a distribution free way of performing hypothesis tests. These tests rely on the condition that the observed data are exchangeable among the groups being tested under the null hypothesis. This assumption is easily…

We consider the problem of inference after model selection under weak assumptions in the time series setting. Even when the data are not independent, we show that sample splitting remains asymptotically valid as long as the process…

Test statistics are often strongly dependent in large-scale multiple testing applications. Most corrections for multiplicity are unduly conservative for correlated test statistics, resulting in a loss of power to detect true positives. We…

This paper proposes a new mutual independence test for a large number of high dimensional random vectors. The test statistic is based on the characteristic function of the empirical spectral distribution of the sample covariance matrix. The…

A distributed binary hypothesis testing problem is studied with one observer and two decision centers. Achievable type-II error exponents are derived for testing against conditional independence when the observer communicates with the two…

In large scale genetic association studies, a primary aim is to test for association between genetic variants and a disease outcome. The variants of interest are often rare, and appear with low frequency among subjects. In this situation,…

I have three goals in this article: (1) To show the enormous potential of bootstrapping and permutation tests to help students understand statistical concepts including sampling distributions, standard errors, bias, confidence intervals,…