Related papers: Paired sample tests in infinite dimensional spaces
Spatial range joins have many applications, including geographic information systems, location-based social networking services, neuroscience, and visualization. However, joins incur not only expensive computational costs but also too large…
We propose a two-sample test for the means of high-dimensional data when the data dimension is much larger than the sample size. Hotelling's classical $T^2$ test does not work for this "large $p$, small $n$" situation. The proposed test…
Statistically equivalent blocks are not frequently considered in the context of nonparametric two-sample hypothesis testing. Despite the limited exposure, this paper shows that a number of classical nonparametric hypothesis tests can be…
Rotationally symmetric distributions on the p-dimensional unit hypersphere, extremely popular in directional statistics, involve a location parameter theta that indicates the direction of the symmetry axis. The most classical way of…
Convex combinations of i.i.d. random variables without a finite mean can behave in a strikingly different way from the finite-mean case: as the weight vector becomes more balanced, the resulting combination may become stochastically larger,…
In public health applications, spatial data collected are often recorded at different spatial scales and over different correlated variables. Spatial change of support is a key inferential problem in these applications and have become…
In this paper, we provide a statistical testing framework to check whether a random sample splitting in a multi-dimensional space is carried out in a valid way, which could be directly applied to A/B testing and multivariate testing to…
Testing the equality of the covariance matrices of two high-dimensional samples is a fundamental inference problem in statistics. Several tests have been proposed but they are either too liberal or too conservative when the required…
This paper considers the problem of testing temporal homogeneity of $p$-dimensional population mean vectors from the repeated measurements of $n$ subjects over $T$ times. To cope with the challenges brought by high-dimensional longitudinal…
Change point tests for abrupt changes in the mean of functional data, i.e., random elements in infinite-dimensional Hilbert spaces, are either based on dimension reduction techniques, e.g., based on principal components, or directly based…
The need to test whether two random vectors are independent has spawned a large number of competing measures of dependence. We are interested in nonparametric measures that are invariant under strictly increasing transformations, such as…
A common heuristic in semi-supervised deep learning (SSDL) is to select unlabelled data based on a notion of semantic similarity to the labelled data. For example, labelled images of numbers should be paired with unlabelled images of…
In this article, we present a nonparametric method for the general two-sample problem involving functional random variables modelled as elements of a separable Hilbert space ${\cal H}$. First, we present a general recipe based on linear…
A variety of statistics based on sample spacings has been studied in the literature for testing goodness-of-fit to parametric distributions. To test the goodness-of-fit to a nonparametric class of univariate shape-constrained densities,…
Inverse normal transformations applied to the partially overlapping samples t-tests by Derrick et.al. (2017) are considered for their Type I error robustness and power. The inverse normal transformation solutions proposed in this paper are…
A new robust pairwise statistic, the pairwise median scaled difference (MSD), is proposed for the detection of anomalous location/uncertainty pairs in heteroscedastic interlaboratory study data with associated uncertainties. The…
We consider the testing and estimation of change-points, locations where the distribution abruptly changes, in a sequence of multivariate or non-Euclidean observations. We study a nonparametric framework that utilizes similarity information…
This article is concerned with simultaneous tests on linear regression coefficients in high-dimensional settings. When the dimensionality is larger than the sample size, the classic $F$-test is not applicable since the sample covariance…
This paper studies one-sided hypothesis testing under random sampling without replacement. That is, when $n+1$ binary random variables $X_1,\ldots, X_{n+1}$ are subject to a permutation invariant distribution and $n$ binary random variables…
We develop a test for spherical symmetry of a multivariate distribution $\Pr$ that works well even when the dimension of the data $d$ is larger than the sample size $n$. We propose a non-negative measure of spherical asymmetry $\zeta(\Pr)$…