Related papers: Local permutation tests for conditional independen…

Often the question arises whether $Y$ can be predicted based on $X$ using a certain model. Especially for highly flexible models such as neural networks one may ask whether a seemingly good prediction is actually better than fitting pure…

Symmetry plays a central role in the sciences, machine learning, and statistics. While statistical tests for the presence of distributional invariance with respect to groups have a long history, tests for conditional symmetry in the form of…

We consider the problem of non-parametric testing of independence of two components of a stationary bivariate spatial process. In particular, we revisit the random shift approach that has become a standard method for testing the independent…

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…

We consider the problem of bounding large deviations for non-i.i.d. random variables that are allowed to have arbitrary dependencies. Previous works typically assumed a specific dependence structure, namely the existence of independent…

Many tools exist to detect dependence between random variables, a core question across a wide range of machine learning, statistical, and scientific endeavors. Although several statistical tests guarantee eventual detection of any…

The paper introduces robust independence tests with non-asymptotically guaranteed significance levels for stochastic linear time-invariant systems, assuming that the observed outputs are synchronous, which means that the systems are driven…

This article addresses the problem of testing the conditional independence of two generic random vectors $X$ and $Y$ given a third random vector $Z$, which plays an important role in statistical and machine learning applications. We propose…

This paper studies permutation tests for regression parameters in a time series setting, where the time series is assumed stationary but may exhibit an arbitrary (but weak) dependence structure. In such a setting, it is perhaps surprising…

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…

For testing two random vectors for independence, we consider testing whether the distance of one vector from a center point is independent from the distance of the other vector from a center point by a univariate test. In this paper we…

Simultaneous inference allows for the exploration of data while deciding on criteria for proclaiming discoveries. It was recently proved that all admissible post-hoc inference methods for true discoveries must employ closed testing. In this…

Experiments often yield non-identically distributed data for statistical analysis. Tests of hypothesis under such set-ups are generally performed using the likelihood ratio test, which is non-robust with respect to outliers and model…

We describe a data-efficient, kernel-based approach to statistical testing of conditional independence. A major challenge of conditional independence testing is to obtain the correct test level (the specified upper bound on the rate of…

The partial copula provides a method for describing the dependence between two random variables $X$ and $Y$ conditional on a third random vector $Z$ in terms of nonparametric residuals $U_1$ and $U_2$. This paper develops a nonparametric…

This paper deals with statistical tests on the components of mixture densities. We propose to test whether the densities of two independent samples of independent random variables $Y_1, ..., Y_n$ and $Z_1, ..., Z_n$ result from the same…

Independence testing plays a central role in statistical and causal inference from observational data. Standard independence tests assume that the data samples are independent and identically distributed (i.i.d.) but that assumption is…

I introduce a simple permutation procedure to test conventional (non-sharp) hypotheses about the effect of a binary treatment in the presence of a finite number of large, heterogeneous clusters when the treatment effect is identified by…

Permutation testing in linear models, where the number of nuisance coefficients is smaller than the sample size, is a well-studied topic. The common approach of such tests is to permute residuals after regressing on the nuisance covariates.…

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…