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Uniform random rotations are a useful primitive in applications such as fast Johnson-Lindenstrauss embeddings, kernel approximation, communication-efficient learning, and recent AI compression pipelines, but they are computationally…
This paper studies distributed binary test of statistical independence under communication (information bits) constraints. While testing independence is very relevant in various applications, distributed independence test is particularly…
Three different permutation test schemes are discussed and compared in the context of the two-sample problem for functional data. One of the procedures was essentially introduced by Lopez-Pintado and Romo (2009), using notions of functional…
The quantum analogue of the equality function, known as the quantum state identity problem, is the task of deciding whether $n$ unknown quantum states are equal or unequal, given the promise that all states are either pairwise orthogonal or…
We consider the problem of estimating the mean of a normal distribution under the following constraint: the estimator can access only a single bit from each sample from this distribution. We study the squared error risk in this estimation…
The focus of this study is to evaluate the effectiveness of Machine Learning (ML) methods for two-sample testing with right-censored observations. To achieve this, we develop several ML-based methods with varying architectures and implement…
Considering multivariate strongly mixing time series, nonparametric tests for a constant copula with specified or unspecified change point (candidate) are derived; the tests are consistent against general alternatives. A tapered block…
Multi-source and multi-modal datasets are increasingly common in scientific research, yet they often exhibit block-wise missingness, where entire modalities are systematically absent in some sources or no single source contains all…
A generalization of Passing-Bablok regression is proposed for comparing multiple measurement methods simultaneously. Possible applications include assay migration studies or interlaboratory trials. When comparing only two methods, the…
We propose a permutation-based method for testing a large collection of hypotheses simultaneously. Our method provides lower bounds for the number of true discoveries in any selected subset of hypotheses. These bounds are simultaneously…
We consider estimation and inference in a linear model with endogenous regressors where the parameters of interest change across two samples. If the first-stage is common, we show how to use this information to obtain more efficient…
In the problem of composite hypothesis testing, identifying the potential uniformly most powerful (UMP) unbiased test is of great interest. Beyond typical hypothesis settings with exponential family, it is usually challenging to prove the…
Non-parametric tests based on permutation, rotation or sign-flipping are examples of group-invariance tests. These tests test invariance of the null distribution under a set of transformations that has a group structure, in the algebraic…
We present the first finite-sample goodness-of-fit test for the mixed membership stochastic block model (MMSBM). Using algebraic statistics theory, we derive a Markov basis that lets a Metropolis-Hastings sampler explore exactly the set of…
The two-trials rule for drug approval requires "at least two adequate and well-controlled studies, each convincing on its own, to establish effectiveness". This is usually implemented by requiring two significant pivotal trials and is the…
A well-known metric for quantifying the similarity between two clusterings is the adjusted mutual information. Compared to mutual information, a corrective term based on random permutations of the labels is introduced, preventing two…
Huffman encoding is often improved by using block codes, for example a 3-block would be an alphabet consisting of each possible combination of three characters. We take the approach of starting with a base alphabet and expanding it to…
The problem of binary hypothesis testing between two probability measures is considered. New sharp bounds are derived for the best achievable error probability of such tests based on independent and identically distributed observations.…
This paper proposes new tests of conditional independence of two random variables given a single-index involving an unknown finite-dimensional parameter. The tests employ Rosenblatt transforms and are shown to be distribution-free while…
In this article, we propose some two-sample tests based on ball divergence and investigate their high dimensional behavior. First, we study their behavior for High Dimension, Low Sample Size (HDLSS) data, and under appropriate regularity…