Related papers: Differentially Private Chi-Squared Hypothesis Test…
We propose generalized portmanteau-type test statistics in the frequency domain to test independence between two stationary time series. The test statistics are formed analogous to the one in Chen and Deo (2004, Econometric Theory 20,…
Analogues of the frequentist chi-square and F tests are proposed for testing goodness-of-fit and consistency for Bayesian models. Simple examples exhibit these tests' detection of inconsistency between consecutive experiments with identical…
In this article, we consider the problem of testing the independence between two random variables. Our primary objective is to develop tests that are highly effective at detecting associations arising from explicit or implicit functional…
We propose a new definition of the chi-square divergence between distributions. Based on convexity properties and duality, this version of the {\chi}^2 is well suited both for the classical applications of the {\chi}^2 for the analysis of…
We consider the identity testing problem - or goodness-of-fit testing problem - in multivariate binomial families, multivariate Poisson families and multinomial distributions. Given a known distribution $p$ and $n$ iid samples drawn from an…
This paper discusses estimation and limited information goodness-of-fit test statistics in factor models for binary data using pairwise likelihood estimation and sampling weights. The paper extends the applicability of pairwise likelihood…
Statistical distances, divergences, and similar quantities have a large history and play a fundamental role in statistics, machine learning and associated scientific disciplines. However, within the statistical literature, this extensive…
In this work, we present a connection between Lipschitz property testing and a relaxed notion of differential privacy, where we assume that the datasets are being sampled from a domain according to some distribution defined on it.…
Statistical hypothesis tests typically use prespecified sample sizes, yet data often arrive sequentially. Interim analyses invalidate classical error guarantees, while existing sequential methods require rigid testing preschedules or incur…
The Newcomb-Benford probability distribution is becoming very popular in many areas using statistics, notably in fraud detection. In such contexts, it is important to be able to determine if a data set arises from this distribution while…
Multivariate analyses play an important role in high energy physics. Such analyses often involve performing an unbinned maximum likelihood fit of a probability density function (p.d.f.) to the data. This paper explores a variety of unbinned…
Users of a personalised recommendation system face a dilemma: recommendations can be improved by learning from data, but only if the other users are willing to share their private information. Good personalised predictions are vitally…
This paper extends our earlier article, "Computing the confidence levels for a root-mean-square test of goodness-of-fit;" unlike in the earlier article, the models in the present paper involve parameter estimation -- both the null and…
Weighted histograms in Monte Carlo simulations are often used for the estimation of probability density functions. They are obtained as a result of random experiments with random events that have weights. In this paper, the bin contents of…
Releasing full data records is one of the most challenging problems in data privacy. On the one hand, many of the popular techniques such as data de-identification are problematic because of their dependence on the background knowledge of…
Differential privacy guarantees allow the results of a statistical analysis involving sensitive data to be released without compromising the privacy of any individual taking part. Achieving such guarantees generally requires the injection…
The comparison of multivariate population means is a central task of statistical inference. While statistical theory provides a variety of analysis tools, they usually do not protect individuals' privacy. This knowledge can create…
An important aspect of multiple hypothesis testing is controlling the significance level, or the level of Type I error. When the test statistics are not independent it can be particularly challenging to deal with this problem, without…
We describe a test statistic for unbinned goodness-of-fit of data in one dimension. The statistic is based on the two-dimensional Random Walk. The rejection power of this test is explored both for simple and compound hypotheses and, for the…
Differential privacy (DP) is a rigorous notion of data privacy, used for private statistics. The canonical algorithm for differentially private mean estimation is to first clip the samples to a bounded range and then add noise to their…