Related papers: A Characterization of Constant-Sample Testable Pro…
A two-sample hypothesis test is a statistical procedure used to determine whether the distributions generating two samples are identical. We consider the two-sample testing problem in a new scenario where the sample measurements (or sample…
Many commonly used test statistics are based on a norm measuring the evidence against the null hypothesis. To understand how the choice of a norm affects power properties of tests in high dimensions, we study the consistency sets of…
The characteristic functional is the infinite-dimensional generalization of the Fourier transform for measures on function spaces. It characterizes the statistical law of the associated stochastic process in the same way as a characteristic…
In property testing, a tester makes queries to (an oracle for) a graph and, on a graph having or being far from having a property P, it decides with high probability whether the graph satisfies P or not. Often, testers are restricted to a…
Assume that we have a random sample from an absolutely continuous distribution (univariate, or multivariate) with a known functional form and some unknown parameters. In this paper, we have studied several parametric tests based on…
We discuss a graph-based approach for testing spatial point patterns. This approach falls under the category of data-random graphs, which have been introduced and used for statistical pattern recognition in recent years. Our goal is to test…
Let $X=\{x_i:i\in\mathbb{Z}\}$, $\dots<x_{i-1}<x_i<x_{i+1}<\dots$, be a sampling set which is separated by a constant $\gamma>0$. Under certain conditions on $\phi$, it is proved that if there exists a positive integer $\nu$ such that…
We propose a series-based nonparametric specification test for a regression function when data are spatially dependent, the `space' being of a general economic or social nature. Dependence can be parametric, parametric with increasing…
The energy test is a powerful binning-free, multi-dimensional and distribution-free tool that can be applied to compare a measurement to a given prediction (goodness-of-fit) or to check whether two data samples originate from the same…
The framework of distribution testing is currently ubiquitous in the field of property testing. In this model, the input is a probability distribution accessible via independently drawn samples from an oracle. The testing task is to…
In this paper, we consider the problem of testing the equality of two multivariate distributions based on geometric graphs constructed using the interpoint distances between the observations. These include the tests based on the minimum…
In this paper, we study the problem of testing the equality of two multivariate distributions. One class of tests used for this purpose utilizes geometric graphs constructed using inter-point distances. So far, the asymptotic theory of…
We consider the problem of testing whether pairs of univariate random variables are associated. Few tests of independence exist that are consistent against all dependent alternatives and are distribution free. We propose novel tests that…
A popular approach for testing if two univariate random variables are statistically independent consists of partitioning the sample space into bins, and evaluating a test statistic on the binned data. The partition size matters, and the…
We develop a monitoring procedure to detect changes in a large approximate factor model. Letting $r$ be the number of common factors, we base our statistics on the fact that the $\left( r+1\right) $-th eigenvalue of the sample covariance…
We study one class of continuous functions $f$ defined on segment $[0,1]$ by equality $$ f(x)=\delta_{\alpha_1(x)1}+\sum^{\infty}_{k=2}\left[\delta_{\alpha_k(x)k}\prod^{k-1}_{j=1}g_{\alpha_j…
We describe a $\tilde{O}(d^{5/6})$-query monotonicity tester for Boolean functions $f:[n]^d \to \{0,1\}$ on the $n$-hypergrid. This is the first $o(d)$ monotonicity tester with query complexity independent of $n$. Motivated by this…
A distance estimator for a graph property $\mathcal{P}$ is an algorithm that given $G$ and $\alpha, \varepsilon >0$ distinguishes between the case that $G$ is $(\alpha-\varepsilon)$-close to $\mathcal{P}$ and the case that $G$ is…
It is commonly known that any Bayesian network can be implemented as a probabilistic program, but the reverse direction is not so clear. In this work, we address the open question to what extent a probabilistic program with user-labelled…
In shape-constrained nonparametric inference, it is often necessary to perform preliminary tests to verify whether a probability mass function (p.m.f.) satisfies qualitative constraints such as monotonicity, convexity, or in general…