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In the present article we introduce a quantum mechanism which is able to describe the creation of correlations in the evaluation of random independent events: such correlations, known as positive and negative recency, correspond…
Testing for association or dependence between pairs of random variables is a fundamental problem in statistics. In some applications, data are subject to selection bias that causes dependence between observations even when it is absent from…
In this paper, we study sequential testing problems with \emph{overlapping} hypotheses. We first focus on the simple problem of assessing if the mean $\mu$ of a Gaussian distribution is smaller or larger than a fixed $\epsilon>0$; if…
We consider the problem of determining feasible systems from a finite set of simulated alternatives with respect to probability constraints, where the observations from stochastic simulations are Bernoulli distributed. Most statistically…
A cornerstone of human statistical learning is the ability to extract temporal regularities / patterns from random sequences. Here we present a method of computing pattern time statistics with generating functions for first-order Markov…
In group sequential designs, where several data looks are conducted for early stopping, we generally assume the vector of test statistics from the sequential analyses follows (at least approximately or asymptotially) a multivariate normal…
We obtain an explicit formula for the variance of the number of $k$-peaks in a uniformly random permutation. This is then used to obtain an asymptotic formula for the variance of the length of longest $k$-alternating subsequence in random…
Analyzing football score data with statistical techniques, we investigate how the highly co-operative nature of the game is reflected in averaged properties such as the distributions of scored goals for the home and away teams. It turns out…
Permutations of correlated sequences of random variables appear naturally in a variety of applications such as graph matching and asynchronous communications. In this paper, the asymptotic statistical behavior of such permuted sequences is…
We propose distribution-free runs-based control charts for detecting location shifts. Using the fact that given the number of total successes, the outcomes of a sequence of Bernoulli trials are random permutations, we are able to control…
In large scale genetic association studies, a primary aim is to test for association between genetic variants and a disease outcome. The variants of interest are often rare, and appear with low frequency among subjects. In this situation,…
This paper studies the problem of finding an anomalous arm in a multi-armed bandit when (a) each arm is a finite-state Markov process, and (b) the arms are restless. Here, anomaly means that the transition probability matrix (TPM) of one of…
In this paper, we consider the nonasymptotic sequential estimation of means of random variables bounded in between zero and one. We have rigorously demonstrated that, in order to guarantee prescribed relative precision and confidence level,…
How can we monitor, in real time, whether one uncertain prospect has any upside over another? To answer this question, we develop a novel family of sequential, anytime-valid tests for stochastic dominance (SD; also known as stochastic…
We consider a permutation method for testing whether observations given in their natural pairing exhibit an unusual level of similarity in situations where any two observations may be similar at some unknown baseline level. Under a null…
Invariance-based randomization tests -- such as permutation tests, rotation tests, or sign changes -- are an important and widely used class of statistical methods. They allow drawing inferences under weak assumptions on the data…
Practical problems with missing data are common, and statistical methods have been developed concerning the validity and/or efficiency of statistical procedures. On a central focus, there have been longstanding interests on the mechanism…
We propose the density ratio permutation test, a hypothesis test that assesses whether the ratio between two densities is proportional to a known function based on independent samples from each distribution. The test uses an efficient…
This paper studies how insurers can chose which claims to investigate for fraud. Given a prediction model, typically only claims with the highest predicted propability of being fraudulent are investigated. We argue that this can lead to…
In this work, Bernoulli's Law of Large Numbers, also known as the Golden theorem, has been extended to study the relations between empirical probability and empirical randomness of an otherwise random experiment. Using the example of a coin…