Related papers: Kernel Tests of Equivalence
Equivalence testing, a fundamental problem in the field of distribution testing, seeks to infer if two unknown distributions on $[n]$ are the same or far apart in the total variation distance. Conditional sampling has emerged as a powerful…
We consider the problem of sequentially testing a simple null hypothesis versus a composite alternative hypothesis that consists of a finite set of densities. We study sequential tests that are based on thresholding of mixture-based…
We propose a test for model specification of a parametric diffusion process based on a kernel estimation of the transitional density of the process. The empirical likelihood is used to formulate a statistic, for each kernel smoothing…
We investigate the discrepancy principle for choosing smoothing parameters for kernel density estimation. The method is based on the distance between the empirical and estimated distribution functions. We prove some new positive and…
We study the problem of testing the equivalence of functional parameters (such as the mean or variance function) in the two sample functional data problem. In contrast to previous work, which reduces the functional problem to a multiple…
We consider goodness-of-fit tests for uniformity of a multinomial distribution by means of tests based on a class of symmetric statistics, defined as the sum of some function of cell-frequencies. We are dealing with an asymptotic regime,…
Consider a setting with multiple units (e.g., individuals, cohorts, geographic locations) and outcomes (e.g., treatments, times, items), where the goal is to learn a multivariate distribution for each unit-outcome entry, such as the…
We study the worst case error of kernel density estimates via subset approximation. A kernel density estimate of a distribution is the convolution of that distribution with a fixed kernel (e.g. Gaussian kernel). Given a subset (i.e. a point…
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…
Much of machine learning relies on comparing distributions with discrepancy measures. Stein's method creates discrepancy measures between two distributions that require only the unnormalized density of one and samples from the other. Stein…
A common challenge in nonparametric inference is its high computational complexity when data volume is large. In this paper, we develop computationally efficient nonparametric testing by employing a random projection strategy. In the…
Model checking plays an important role in linear regression as model misspecification seriously affects the validity and efficiency of regression analysis. In practice, model checking is often performed by subjectively evaluating the plot…
We introduce a new goodness-of-fit test for count data on $\mathbb{N}$ for the Zeta distribution with unknown parameter. The test is built on a Stein-type characterization that uses, as Stein operator, the infinitesimal generator of a…
We provide a unifying framework linking two classes of statistics used in two-sample and independence testing: on the one hand, the energy distances and distance covariances from the statistics literature; on the other, distances between…
We propose a new test to address the nonparametric Behrens-Fisher problem involving different distribution functions in the two samples. Our procedure tests the null hypothesis $\mathcal{H}_0: \theta = \frac{1}{2}$, where $\theta = P(X<Y) +…
Kernel density estimation is a technique for approximating probability distributions. Here, it is applied to the calculation of mutual information on a metric space. This is motivated by the problem in neuroscience of calculating the mutual…
Testing hypotheses of goodness-of-fit about mixture distributions on the basis of independent but not necessarily identically distributed random vectors is considered. The hypotheses are given by a specific distribution or by a family of…
Achieving error rates that meet or exceed the fault-tolerance threshold is a central goal for quantum computing experiments, and measuring these error rates using randomized benchmarking is now routine. However, direct comparison between…
When comparing two distributions, it is often helpful to learn at which quantiles or values there is a statistically significant difference. This provides more information than the binary "reject" or "do not reject" decision of a global…
Bell tests---the experimental demonstration of a Bell inequality violation---are central to understanding the foundations of quantum mechanics, underpin quantum technologies, and are a powerful diagnostic tool for technological developments…