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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…

Statistics Theory · Mathematics 2023-01-04 Jin-Ting Zhang , Jingyi Wang , Tianming Zhu

We consider parametric hypotheses testing for multidimensional ergodic diffusion processes observed at discrete time. We propose a family of test statistics, related to the so called $\phi$-divergence measures. By taking into account the…

Statistics Theory · Mathematics 2011-11-14 Alessandro De Gregorio , Stefano Iacus

Conditional independence (CI) tests are widely used in statistical data analysis, e.g., they are the building block of many algorithms for causal graph discovery. The goal of a CI test is to accept or reject the null hypothesis that $X…

Machine Learning · Statistics 2024-03-26 Iden Kalemaj , Shiva Prasad Kasiviswanathan , Aaditya Ramdas

Pearson's chi-squared test, from 1900, is the standard statistical tool for "hypothesis testing on distributions": namely, given samples from an unknown distribution $Q$ that may or may not equal a hypothesis distribution $P$, we want to…

Statistics Theory · Mathematics 2023-10-17 Trung Dang , Walter McKelvie , Paul Valiant , Hongao Wang

Reduced chi-squared is a very popular method for model assessment, model comparison, convergence diagnostic, and error estimation in astronomy. In this manuscript, we discuss the pitfalls involved in using reduced chi-squared. There are two…

Instrumentation and Methods for Astrophysics · Physics 2010-12-20 Rene Andrae , Tim Schulze-Hartung , Peter Melchior

Differential privacy has emerged as an significant cornerstone in the realm of scientific hypothesis testing utilizing confidential data. In reporting scientific discoveries, Bayesian tests are widely adopted since they effectively…

Machine Learning · Statistics 2025-12-22 Abhisek Chakraborty , Saptati Datta

Pearson's Chi-square test is a widely used tool for analyzing categorical data, yet its statistical power has remained theoretically underexplored. Due to the difficulties in obtaining its power function in the usual manner, Cochran (1952)…

Methodology · Statistics 2024-09-24 Qingyang Zhang

We propose a general optimization-based framework for computing differentially private M-estimators and a new method for constructing differentially private confidence regions. Firstly, we show that robust statistics can be used in…

Statistics Theory · Mathematics 2023-12-14 Marco Avella-Medina , Casey Bradshaw , Po-Ling Loh

In this paper, we consider privacy against hypothesis testing adversaries within a non-stochastic framework. We develop a theory of non-stochastic hypothesis testing by borrowing the notion of uncertain variables from non-stochastic…

Information Theory · Computer Science 2019-04-17 Farhad Farokhi

We provide improved differentially private algorithms for identity testing of high-dimensional distributions. Specifically, for $d$-dimensional Gaussian distributions with known covariance $\Sigma$, we can test whether the distribution…

Data Structures and Algorithms · Computer Science 2022-07-26 Shyam Narayanan

We propose a two-sample testing procedure based on learned deep neural network representations. To this end, we define two test statistics that perform an asymptotic location test on data samples mapped onto a hidden layer. The tests are…

Machine Learning · Statistics 2020-03-11 Matthias Kirchler , Shahryar Khorasani , Marius Kloft , Christoph Lippert

We present new families of goodness-of-fit tests of uniformity on a full-dimensional set $W\subset\R^d$ based on statistics related to edge lengths of random geometric graphs. Asymptotic normality of these statistics is proven under the…

Statistics Theory · Mathematics 2020-07-20 Bruno Ebner , Franz Nestmann , Matthias Schulte

A new test statistic based on success runs of weighted deviations is introduced. Its use for observations sampled from independent normal distributions is worked out in detail. It supplements the classic $\chi^{2}$ test which ignores the…

Statistics Theory · Mathematics 2017-04-10 Frederik Beaujean , Allen Caldwell

Privacy protection methods, such as differentially private mechanisms, introduce noise into resulting statistics which often produces complex and intractable sampling distributions. In this paper, we propose a simulation-based "repro…

Statistics Theory · Mathematics 2024-11-07 Jordan Awan , Zhanyu Wang

The main goal of this article is to study how an auxiliary information can be used to improve the efficiency of two famous statistical tests: the $ Z$-test and the chi-square test. Many definitions of auxiliary information can be found in…

Statistics Theory · Mathematics 2021-09-03 Mickael Albertus

Differential privacy is a cryptographically-motivated approach to privacy that has become a very active field of research over the last decade in theoretical computer science and machine learning. In this paradigm one assumes there is a…

Machine Learning · Computer Science 2023-08-02 Marco Avella-Medina

Modern society generates an incredible amount of data about individuals, and releasing summary statistics about this data in a manner that provably protects individual privacy would offer a valuable resource for researchers in many fields.…

Cryptography and Security · Computer Science 2018-02-21 Zachary Campbell , Andrew Bray , Anna Ritz , Adam Groce

We present a generic framework for creating differentially private versions of any hypothesis test in a black-box way. We analyze the resulting tests analytically and experimentally. Most crucially, we show good practical performance for…

Methodology · Statistics 2023-02-09 Zeki Kazan , Kaiyan Shi , Adam Groce , Andrew Bray

We describe likelihood-based statistical tests for use in high energy physics for the discovery of new phenomena and for construction of confidence intervals on model parameters. We focus on the properties of the test procedures that allow…

Data Analysis, Statistics and Probability · Physics 2013-06-25 Glen Cowan , Kyle Cranmer , Eilam Gross , Ofer Vitells

We introduce new estimates and tests of independence in copula models with unknown margins using $\phi$-divergences and the duality technique. The asymptotic laws of the estimates and the test statistics are established both when the…

Statistics Theory · Mathematics 2019-03-06 Salim Bouzebda , Amor Keziou