Related papers: Inference via Randomized Test Statistics

In this paper we investigate the asymptotic distribution of likelihood ratio tests in models with several groups, when the number of groups converges with the dimension and sample size to infinity. We derive central limit theorems for the…

This paper is concerned with Spearman's correlation matrices under large dimensional regime, in which the data dimension diverges to infinity proportionally with the sample size. We establish the central limit theorem for the linear…

Given an i.i.d. sample drawn from a density $f$, we propose to test that $f$ equals some prescribed density $f_0$ or that $f$ belongs to some translation/scale family. We introduce a multiple testing procedure based on an estimation of the…

Motivated by the problem of testing tetrad constraints in factor analysis, we study the large-sample distribution of Wald statistics at parameter points at which the gradient of the tested constraint vanishes. When based on an…

We establish the rate of convergence of distributions of sums of independent identically distributed random variables to the Gaussian distribution in terms of truncated pseudomoments by implementing the idea of Yu. Studnyev for getting…

We present some product representations for random variables with the Linnik, Mittag-Leffler and Weibull distributions and establish the relationship between the mixing distributions in these representations. Based on these representations,…

We study a random partial covering model on the $(d-1)$-dimensional unit sphere, where $N$ spherical caps are placed independently and uniformly at random, each covering a surface fraction of $1/N$. This model provides a continuous…

We study the asymptotic distributions of the number of crossings and the number of simple chords in a random chord diagram. Using size-bias coupling and Stein's method, we obtain bounds on the Kolmogorov distance between the distribution of…

In this paper we present randomization methods to enhance the accuracy of the central limit theorem (CLT) based inferences about the population mean $\mu$. We introduce a broad class of randomized versions of the Student $t$-statistic, the…

We study the limiting behavior of smooth linear statistics of the spectrum of random permutation matrices in the mesoscopic regime, when the permutation follows one of the Ewens measures on the symmetric group. If we apply a smooth enough…

Let $f:[0,1)^d \to {\mathbb R}$ be an integrable function. An objective of many computer experiments is to estimate $\int_{[0,1)^d} f(x) dx$ by evaluating f at a finite number of points in [0,1)^d. There is a design issue in the choice of…

This paper investigates robust versions of the general empirical risk minimization algorithm, one of the core techniques underlying modern statistical methods. Success of the empirical risk minimization is based on the fact that for a…

Let $\{X_n;n\ge 1\}$ be a sequence of independent random variables on a probability space $(\Omega, \mathcal{F}, P)$ and $S_n=\sum_{k=1}^n X_k$. It is well-known that the almost sure convergence, the convergence in probability and the…

We consider a classical model related to an empirical distribution function $ F_n(t)=\frac{1}{n}\sum_{k=1}^nI_{\{\xi_k\le t\}}$ of $(\xi_k)_{i\ge 1}$ -- i.i.d. sequence of random variables, supported on the interval $[0,1]$, with continuous…

Randomization-based inference commonly relies on grid search methods to construct confidence intervals by inverting hypothesis tests over a range of parameter values. While straightforward, this approach is computationally intensive and can…

In situations where it is difficult to enroll patients in randomized controlled trials, external data can improve efficiency and feasibility. In such cases, adaptive trial designs could be used to decrease enrollment in the control arm of…

This paper concerns the construction of tests for universal hypothesis testing problems, in which the alternate hypothesis is poorly modeled and the observation space is large. The mismatched universal test is a feature-based technique for…

We prove a convergence theorem for U-statistics of degree two, where the data dimension $d$ is allowed to scale with sample size $n$. We find that the limiting distribution of a U-statistic undergoes a phase transition from the…

We analyzed the effect of the deviation of the exact distribution of the p-values from the uniform distribution on the Kolmogorov-Smirnov (K-S) test that was implemented as the second-level randomness test. We derived an inequality that…

In this paper new test statistics are introduced and studied for the important problem of testing hypothesis that involves inequality constraint on proportions when the sample comes from independent binomial random variables: Wald type and…