Related papers: A test against trend in random sequences
Let $S_n$ denote the set of permutations of $[n]:=\{1,\cdots, n\}$, and denote a permutation $\sigma\in S_n$ by $\sigma=\sigma_1\sigma_2\cdots \sigma_n$. For $l\ge2$ an integer, let $A^{(n)}_{l;k}\subset S_n$ denote the event that the set…
Selective information transfer in spin ring networks by energy landscape shaping control has the property that the error 1-prob, where prob is the transfer success probability, and the sensitivity of the error to spin coupling uncertainties…
We consider a random permutation drawn from the set of 132-avoiding permutations of length $n$ and show that the number of occurrences of another pattern $\sigma$ has a limit distribution, after scaling by $n^{\lambda(\sigma)/2}$ where…
The combinatorial theory for the set of parity alternating permutations is expounded. In view of the numbers of ascents and inversions, several enumerative aspects of the set are investigated. In particular, it is shown that signed Eulerian…
The paper deals with a new class of random walks strictly connected with the Pareto distribution. We consider stochastic processes in the sense of generalized convolution or weak generalized convolution following the idea given in [1]. The…
Kendall rank correlation coefficient is used to measure the ordinal association between two measurements. In this paper, we introduce the Concordance coefficient as a generalization of the Kendall rank correlation, and illustrate its use to…
Kendall's tau and conditional Kendall's tau matrices are multivariate (conditional) dependence measures between the components of a random vector. For large dimensions, available estimators are computationally expensive and can be improved…
We consider the conditional randomization test as a way to account for covariate imbalance in randomized experiments. The test accounts for covariate imbalance by comparing the observed test statistic to the null distribution of the test…
By a classical principle of probability theory, sufficiently thin subsequences of general sequences of random variables behave like i.i.d.\ sequences. This observation not only explains the remarkable properties of lacunary trigonometric…
Permutation patterns and pattern avoidance are central, well-studied concepts in combinatorics and computer science. Given two permutations $\tau$ and $\pi$, the pattern matching problem (PPM) asks whether $\tau$ contains $\pi$. This…
We consider a quantum system that is being continuously monitored, giving rise to a measurement signal. From such a stream of data, information needs to be inferred about the underlying system's dynamics. Here we focus on hypothesis testing…
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…
This paper investigates a statistical procedure for testing the equality of two independent estimated covariance matrices when the number of potentially dependent data vectors is large and proportional to the size of the vectors, that is,…
Selecting N random points in a unit square corresponds to selecting a random permutation. By putting 5 types of symmetry restrictions on the points, we obtain subsets of permutations : involutions, signed permutations and signed…
We study the longest increasing subsequence problem for random permutations avoiding the pattern $312$ and another pattern $\tau$ under the uniform probability distribution. We determine the exact and asymptotic formulas for the average…
We describe a modified sequential probability ratio test that can be used to reduce the average sample size required to perform statistical hypothesis tests at specified levels of significance and power. Examples are provided for $z$ tests,…
Sequential monitoring in clinical trials is often employed to allow for early stopping and other interim decisions, while maintaining the type I error rate. However, sequential monitoring is typically described only in the context of a…
In many applied sciences a popular analysis strategy for high-dimensional data is to fit many multivariate generalized linear models in parallel. This paper presents a novel approach to address the resulting multiple testing problem by…
In this paper we propose several variants to perform the independence test between two random elements based on recurrence rates. We will show how to calculate the test statistic in each one of these cases. From simulations we obtain that…
We study a class of hypothesis testing problems in which, upon observing the realization of an $n$-dimensional Gaussian vector, one has to decide whether the vector was drawn from a standard normal distribution or, alternatively, whether…