Related papers: Testing equality of functions under monotonicity c…

Consider a monotone Boolean function $f:\{0,1\}^n\to\{0,1\}$ and the canonical monotone coupling $\{\eta_p:p\in[0,1]\}$ of an element in $\{0,1\}^n$ chosen according to product measure with intensity $p\in[0,1]$. The random point…

We show that every algorithm for testing $n$-variate Boolean functions for monotonicity must have query complexity $\tilde{\Omega}(n^{1/4})$. All previous lower bounds for this problem were designed for non-adaptive algorithms and, as a…

A probability distribution over the Boolean cube is monotone if flipping the value of a coordinate from zero to one can only increase the probability of an element. Given samples of an unknown monotone distribution over the Boolean cube, we…

We propose a new framework for the simultaneous inference of monotone and smoothly time-varying functions under complex temporal dynamics. This will be done utilizing the monotone rearrangement and the nonparametric estimation. We…

We establish new upper and lower bounds on the number of queries required to test convexity of functions over various discrete domains. 1. We provide a simplified version of the non-adaptive convexity tester on the line. We re-prove the…

This paper considers inference for conditional moment inequality models using a multiscale statistic. We derive the asymptotic distribution of this test statistic and use the result to propose feasible critical values that have a simple…

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 present a unified approach to goodness-of-fit testing in $\mathbb{R}^d$ and on lower-dimensional manifolds embedded in $\mathbb{R}^d$ based on sums of powers of weighted volumes of $k$-th nearest neighbor spheres. We prove asymptotic…

This paper proposes novel tests for the absence of jumps in a univariate semimartingale and for the absence of common jumps in a bivariate semimartingale. Our methods rely on ratio statistics of power variations based on irregular…

In this article we prove a generalization of the Ejsmont characterization of the multivariate normal distribution. Based on it, we propose a new test for independence and normality. The test uses an integral of the squared modulus of the…

We study the problem of testing whether a function f:R^n->R is linear (i.e., both additive and homogeneous) in the distribution-free property testing model, where the distance between functions is measured with respect to an unknown…

Starting from the Davenport-Heilbronn function equation: $f(s) = X(s) f(1-s)$, we discover the four properties of the meromorphic function $X(s)$ defined as the ratio of the Davenport-Heilbronn functions: $\frac{f(s)}{f(1-s)} = X(s)$, and…

Suppose that we are interested in the comparison of two independent categorical variables. Suppose also that the population is divided into subpopulations or groups. Notice that the distribution of the target variable may vary across…

For the multi-sample equal covariance function (ECF) testing problem, Zhang (2013) proposed an $L^{2}$-norm based test. However, its asymptotic power and finite sample performance have not been studied. In this paper, its asymptotic power…

Data with multiple functional recordings at each observational unit are increasingly common in various fields including medical imaging and environmental sciences. To conduct inference for such observations, we develop a paired two-sample…

Measuring the (causal) direction and strength of dependence between two variables (events), Xi and Xj , is fundamental for all science. Our survey of decades-long literature on statistical dependence reveals that most assume symmetry in the…

We study the equivalence testing problem where the goal is to determine if the given two unknown distributions on $[n]$ are equal or $\epsilon$-far in the total variation distance in the conditional sampling model (CFGM, SICOMP16; CRS,…

A univariate continuous function can always be decomposed as the sum of a non-increasing function and a non-decreasing one. Based on this property, we propose a non-parametric regression method that combines two spline-fitted monotone…

We study the comparison problem of distribution equality between two random samples under a right censoring scheme. To address this problem, we design a series of tests based on energy distance and kernel mean embeddings. We calibrate our…

A recent asymptotic expansion for the positive zeros $x=j_{\nu,m}$ ($m=1,2,3,\ldots$) of the Bessel function of the first kind $J_{\nu}(x)$ is studied, where the order $\nu$ is positive. Unlike previous well-known expansions in the…