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We consider a Kendall's tau measure between a binary group indicator and the continuous variable under investigation to develop a thorough two-sample comparison procedure. The measure serves as a useful alternative to the hazard ratio whose…
The paper provides a simpler method for proving a delicate inequality that was used by Achlioptis and Naor to establish asymptotic concentration for chromatic numbers of Erdos-Renyi random graphs. The simplifications come from two new…
We extend Stanley's work on alternating permutations with extremal number of fixed points in two directions: first, alternating permutations are replaced by permutations with a prescribed descent set; second, instead of simply counting…
In this paper we study the inverse of so-called unfair permutations, and explore various properties of them. Our investigation begins with comparing this class of permutations with uniformly random permutations, and showing that they behave…
We apply covariate adjustment to the Wincoxon two sample statistic and Wincoxon-Mann-Whitney test in comparing two treatments. The covariate adjustment through calibration not only improves efficiency in estimation/inference but also widens…
Given a permutation statistic $\operatorname{st}$, define its inverse statistic $\operatorname{ist}$ by $\operatorname{ist}(\pi):=\operatorname{st}(\pi^{-1})$. We give a general approach, based on the theory of symmetric functions, for…
We study (asymmetric) $U$-statistics based on a stationary sequence of $m$-dependent variables; moreover, we consider constrained $U$-statistics, where the defining multiple sum only includes terms satisfying some restrictions on the gaps…
The purpose of this article is to present a general method to find limiting laws for some renormalized statistics on random permutations. The model considered here is Ewens sampling model, which generalizes uniform random permutations. We…
Various statistical tests have been developed for testing the equality of means in matched pairs with missing values. However, most existing methods are commonly based on certain distributional assumptions such as normality, 0-symmetry or…
Upper and lower bounds are obtained for the joint entropy of a collection of random variables in terms of an arbitrary collection of subset joint entropies. These inequalities generalize Shannon's chain rule for entropy as well as…
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…
Concentration results and probabilistic analysis for combinatorial problems like the TSP, MWST, graph coloring have received much attention, but generally, for i.i.d. samples (i.i.d. points in the unit square for the TSP, for example).…
In this paper, we have established a new framework of truncated inverse sampling for estimating mean values of non-negative random variables such as binomial, Poisson, hyper-geometrical, and bounded variables. We have derived explicit…
Composite endpoints are increasingly used in clinical trials to capture treatment effects across multiple or hierarchically ordered outcomes. Although inference procedures based on win statistics, such as the win ratio, win odds, and net…
This paper first introduces a refined version of the Azuma-Hoeffding inequality for discrete-parameter martingales with uniformly bounded jumps. The refined inequality is used to revisit the large deviations analysis of binary hypothesis…
The advent of modern data collection and processing techniques has seen the size, scale, and complexity of data grow exponentially. A seminal step in leveraging these rich datasets for downstream inference is understanding the…
We prove a general transfer theorem for multivariate random sequences with independent random indexes in the double array limit setting. We also prove its partial inverse providing necessary and sufficient conditions for the convergence of…
This paper develops methods to study the distribution of Eulerian statistics defined by second-order recurrence relations. We define a random process to decompose the statistics over compositions of integers. It is shown that the numbers of…
This paper derives exponential tail bounds and polynomial moment inequalities for the spectral norm deviation of a random matrix from its mean value. The argument depends on a matrix extension of Stein's method of exchangeable pairs for…
We develop large sample theory for merged data from multiple sources. Main statistical issues treated in this paper are (1) the same unit potentially appears in multiple datasets from overlapping data sources, (2) duplicated items are not…