Related papers: A Characterization of Constant-Sample Testable Pro…

Let $X_1,\ldots,X_n$ be an i.i.d. sample from symmetric stable distribution with stability parameter $\alpha$ and scale parameter $\gamma$. Let $\varphi_n$ be the empirical characteristic function. We prove an uniform large deviation…

We theoretically analyze the problem of testing for $p$-hacking based on distributions of $p$-values across multiple studies. We provide general results for when such distributions have testable restrictions (are non-increasing) under the…

This work includes a new characterization of the multivariate normal distribution. In particular, it is shown that a positive density function $f$ is Gaussian if and only if the $f(x+ y)/f(x)$ is convex in $x$ for every $y$. This result has…

In this paper we prove a characterization of continuity for polynomials on a normed space. Namely, we prove that a polynomial is continuous if and only if it maps compact sets into compact sets. We also provide a partial answer to the…

The random coefficients model is an extension of the linear regression model that allows for unobserved heterogeneity in the population by modeling the regression coefficients as random variables. Given data from this model, the statistical…

We consider the problem of determining which classes of functions can be tested more efficiently than they can be learned, in the distribution-free sample-based model that corresponds to the standard PAC learning setting. Our main result…

This paper studies model checking for general parametric regression models having no dimension reduction structures on the predictor vector. Using any U-statistic type test as an initial test, this paper combines the sample-splitting and…

Randomization tests rely on simple data transformations and possess an appealing robustness property. In addition to being finite-sample valid if the data distribution is invariant under the transformation, these tests can be asymptotically…

The prevalence of multivariate space-time data collected from monitoring networks and satellites, or generated from numerical models, has brought much attention to multivariate spatio-temporal statistical models, where the covariance…

Drawing on some recent results that provide the formalism necessary to definite stationarity for infinite random graphs, this paper initiates the study of statistical and learning questions pertaining to these objects. Specifically, a…

Parameter testing algorithms are using constant number of queries to estimate the value of a certain parameter of a very large finite graph. It is well-known that graph parameters such as the independence ratio or the edit-distance from…

This paper focuses on the problem of testing the null hypothesis that the regression functions of several populations are equal under a general nonparametric homoscedastic regression model. It is well known that linear kernel regression…

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,…

We study distribution testing in the standard access model and the conditional access model when the memory available to the testing algorithm is bounded. In both scenarios, the samples appear in an online fashion and the goal is to test…

In the matter of selection of sample time points for the estimation of the power spectral density of a continuous time stationary stochastic process, irregular sampling schemes such as Poisson sampling are often preferred over regular…

Let $K$ be a field of characteristic $0$, and let $k \geq 2$ be an integer. We prove that every $K$-linear bijection $f \colon K[X] \to K[X]$ strongly preserving the set of $k$-free polynomials (or the set of polynomials with a $k$-fold…

In the problem of high-dimensional convexity testing, there is an unknown set $S \subseteq \mathbb{R}^n$ which is promised to be either convex or $\varepsilon$-far from every convex body with respect to the standard multivariate normal…

Let $\mathcal{F}$ be a collection of $r$-uniform hypergraphs, and let $0 < p < 1$. It is known that there exists $c = c(p,\mathcal{F})$ such that the probability of a random $r$-graph in $G(n,p)$ not containing an induced subgraph from…

We study the frequentist properties of Bayesian statistical inference for the stochastic block model, with an unknown number of classes of varying sizes. We equip the space of vertex labellings with a prior on the number of classes and,…

Statistical inference for stochastic processes with time-varying spectral characteristics has received considerable attention in recent decades. We develop a nonparametric test for stationarity against the alternative of a smoothly…