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In this note, we investigate fundamental relations between exploration processes in random graphs, and branching processes. We formulate a class of models that we call {\em rank-$k$ random graphs}, and that are special in that their…
We consider the problem of computing the joint distribution of order statistics of stochastically independent random variables in one- and two-group models. While recursive formulas for evaluating the joint cumulative distribution function…
We propose a simple yet powerful test statistic to quantify the discrepancy between two conditional distributions. The new statistic avoids the explicit estimation of the underlying distributions in highdimensional space and it operates on…
In this article, we consider the problem of testing whether two latent position random graphs are correlated. We propose a test statistic based on the kernel method and introduce the estimation procedure based on the spectral decomposition…
What proportion of treated units actually benefited from an experimental intervention? What is the median or the largest individual treatment effect? This paper develops methods for answering such questions about the distribution of…
Latent variable models are well-known to suffer from rank deficiencies, causing problems with convergence and stability. Such problems are compounded in the "reduced-group split-ballot multitrait-multimethod model", which omits a set of…
In this paper we study the problem of testing the null hypothesis that errors from k independent parametrically specified generalized autoregressive conditional heteroskedasticity (GARCH) models have the same distribution versus a general…
Testing for normality is a widely used procedure in statistics and data analysis, often applied prior to employing methods that rely on the assumption of normally distributed data. While several existing tests target distributional…
Assume that we have a random sample from an absolutely continuous distribution (univariate, or multivariate) with a known functional form and some unknown parameters. In this paper, we have studied several parametric tests based on…
Non-deterministic measurements are common in real-world scenarios: the performance of a stochastic optimization algorithm or the total reward of a reinforcement learning agent in a chaotic environment are just two examples in which…
We consider the problem of testing whether pairs of univariate random variables are associated. Few tests of independence exist that are consistent against all dependent alternatives and are distribution free. We propose novel tests that…
Stochastic comparisons of series and parallel systems are important in many areas of engineering, operations research and reliability analysis. These comparisons allow for the evaluation of the performance and reliability of systems under…
This paper deals with order identification for nested models in the i.i.d. framework. We study the asymptotic efficiency of two generalized likelihood ratio tests of the order. They are based on two estimators which are proved to be…
We investigate properties of a bootstrap-based methodology for testing hypotheses about equality of certain characteristics of the distributions between different populations in the context of functional data. The suggested testing…
We study the problem of conditional two-sample testing, which aims to determine whether two populations have the same distribution after accounting for confounding factors. This problem commonly arises in various applications, such as…
There exist a number of tests for assessing the nonparametric heteroscedastic location-scale assumption. Here we consider a goodness-of-fit test for the more general hypothesis of the validity of this model under a parametric functional…
Learning-based low rank approximation algorithms can significantly improve the performance of randomized low rank approximation with sketch matrix. With the learned value and fixed non-zero positions for sketch matrices from learning-based…
In this article, we focus on the problem of testing the equality of several high dimensional mean vectors with unequal covariance matrices. This is one of the most important problem in multivariate statistical analysis and there have been…
This paper addresses the general problem of modelling and learning rank data with ties. We propose a probabilistic generative model, that models the process as permutations over partitions. This results in super-exponential combinatorial…
We propose a two-sample test for high-dimensional means that requires neither distributional nor correlational assumptions, besides some weak conditions on the moments and tail properties of the elements in the random vectors. This…