Related papers: A test against trend in random sequences
We present a sequential version of the kernelized Stein discrepancy goodness-of-fit test, which allows for conducting goodness-of-fit tests for unnormalized densities that are continuously monitored and adaptively stopped. That is, the…
Distinguishing between uniform and non-uniform sample distributions is a common problem in directional data analysis; however for many tests, non-uniform distributions exist that fail uniformity rejection. By merging directional statistics…
Symmetry plays a central role in the sciences, machine learning, and statistics. While statistical tests for the presence of distributional invariance with respect to groups have a long history, tests for conditional symmetry in the form of…
In this paper, we derive power guarantees of some sequential tests for bounded mean under general alternatives. We focus on testing procedures using nonnegative supermartingales which are anytime valid and consider alternatives which…
In the last decade a huge amount of articles has been published studying pattern avoidance on permutations. From the point of view of enumeration, typically one tries to count permutations avoiding certain patterns according to their…
Understanding the correlation between two different scores for the same set of items is a common problem in information retrieval, and the most commonly used statistics that quantifies this correlation is Kendall's $\tau$. However, the…
The extension of pattern avoidance from ordinary permutations to those on multisets gave birth to several interesting enumerative results. We study permutations on regular multisets, i.e., multisets in which each element occurs the same…
In this paper, we propose a general method for testing composite hypotheses. Our idea is to use confidence limits to define stopping and decision rules. The requirements of operating characteristic function can be satisfied by adjusting the…
We determine a set of permutation patterns $q$ so that the number of permutations with $r$ occurrences of $q$ is asymptotically $n^r$ times the number of permutations avoiding $q$, partially settling a conjecture of Conway and Guttman. We…
A generalization of the Seidel-Entringer-Arnold method for calculating the alternating permutation numbers (or secant-tangent numbers) leads to a new operation on integer sequences, the Boustrophedon transform.
We study the distribution of cycle lengths in models of nonuniform random permutations with cycle weights. We identify several regimes. Depending on the weights, the length of typical cycles grows like the total number $n$ of elements, or a…
We consider the problem of sequentially testing for changes in the mean parameter of a time series, compared to a benchmark period. Most tests in the literature focus on the null hypothesis of a constant mean versus the alternative of a…
We consider the sequential composite binary hypothesis testing problem in which one of the hypotheses is governed by a single distribution while the other is governed by a family of distributions whose parameters belong to a known set…
We combinatorially prove that the number $R(n,k)$ of permutations of length $n$ having $k$ runs is a log-concave sequence in $k$, for all $n$. We also give a new combinatorial proof for the log-concavity of the Eulerian numbers.
The Armitage test for linear trend in proportions can be modified using the multiple marginal model approach for three regression models with arithmetic, ordinal and logarithmic dose scores simultaneously, to be powerful against a wide…
This work is concerned with the limiting spectral distribution of rank-based dependency measures in high dimensions. We provide distribution-free results for multivariate empirical versions of Kendall's $\tau$ and Spearman's $\rho$ in a…
We study the adversarial binary hypothesis testing problem in the sequential setting. Associated with each hypothesis is a closed, convex set of distributions. Given the hypothesis, each observation is generated according to a distribution…
Permutations are usually enumerated by size, but new results can be found by enumerating them by inversions instead, in which case one must restrict one's attention to indecomposable permutations. In the style of the seminal paper by Simion…
We describe two families of statistical tests to detect partial correlation in vectorial timeseries. The tests measure whether an observed timeseries Y can be predicted from a second series X, even after accounting for a third series Z…
We prove recursive formulas for $\tau_d$, the number of degree $d$ elliptic curves with fixed j-invariant in P^n. We use analysis to relate the classical invariant $\tau_d$ to the genus one perturbed invariant $RT_{1,d}$ defined recently by…