Related papers: Breakdown of statistical inference from some rando…
In quantum physics, all measured observables are subject to statistical uncertainties, which arise from the quantum nature as well as the experimental technique. We consider the statistical uncertainty of the so-called sampling method, in…
Spectral clustering is a popular unsupervised learning technique which is able to partition unlabelled data into disjoint clusters of distinct shapes. However, the data under consideration are often experimental data, implying that the data…
We study the problem of estimating finite sample confidence intervals of the mean of a normal population under the constraint of differential privacy. We consider both the known and unknown variance cases and construct differentially…
In this paper we use a well know method in statistics, the $\delta$-method, to provide an asymptotic distribution for the Mutual Information, and construct and independence test based on it. Interesting connections are found with the…
When reporting statistics from simulations of statistically stationary chaotic phenomenon, it is important to verify that the simulations are time-converged. This condition is connected with the statistical error or number of digits with…
This paper explores the effects of simulated moments on the performance of inference methods based on moment inequalities. Commonly used confidence sets for parameters are level sets of criterion functions whose boundary points may depend…
Causal discovery methods based on the PC algorithm are proven to be sound if all structural assumptions are fulfilled and all conditional independence tests are correct. This idealized setting is rarely given in real data. In this work, we…
Many important problems in psychology and biomedical studies require testing for overdispersion, correlation and heterogeneity in mixed effects and latent variable models, and score tests are particularly useful for this purpose. But the…
The increased availability of massive data sets provides a unique opportunity to discover subtle patterns in their distributions, but also imposes overwhelming computational challenges. To fully utilize the information contained in big…
For linear models with spatial errors, the empirical likelihood ratio statistics are constructed for the parameters of the models. It is shown that the limiting distributions of the empirical likelihood ratio statistics are chi-squared…
A nonparametric anomalous hypothesis testing problem is investigated, in which there are totally n sequences with s anomalous sequences to be detected. Each typical sequence contains m independent and identically distributed (i.i.d.)…
We build on recent works on Stein's method for functions of multivariate normal random variables to derive bounds for the rate of convergence of some asymptotically chi-square distributed statistics. We obtain some general bounds and…
This paper is concerned with the problem of comparing the population means of two groups of independent observations. An approximate randomization test procedure based on the test statistic of Chen and Qin (2010) is proposed. The asymptotic…
Testing hypothesis of independence between two random elements on a joint alphabet is a fundamental exercise in statistics. Pearson's chi-squared test is an effective test for such a situation when the contingency table is relatively small.…
The question of testing for equality in distribution between two linear models, each consisting of sums of distinct discrete independent random variables with unequal numbers of observations, has emerged from the biological research. In…
Benchmarking studies in computational chemistry use reference datasets to assess the accuracy of a method through error statistics. The commonly used error statistics, such as the mean signed and mean unsigned errors, do not inform…
Constructing tests or confidence regions that control over the error rates in the long-run is probably one of the most important problem in statistics. Yet, the theoretical justification for most methods in statistics is asymptotic. The…
Based on the median and the median absolute deviation estimators, and the Hodges-Lehmann and Shamos estimators, robustified analogues of the conventional $t$-test statistic are proposed. The asymptotic distributions of these statistics are…
The purpose of this paper is to propose methodologies for statistical inference of low-dimensional parameters with high-dimensional data. We focus on constructing confidence intervals for individual coefficients and linear combinations of…
In this paper, we address the problem of conducting statistical inference in settings involving large-scale data that may be high-dimensional and contaminated by outliers. The high volume and dimensionality of the data require distributed…