相关论文: An asymptotic Peskun ordering and its application …
This paper provides conditions under which subsampling and the bootstrap can be used to construct estimators of the quantiles of the distribution of a root that behave well uniformly over a large class of distributions $\mathbf{P}$. These…
In many empirical studies of a large two-sided matching market (such as in a college admissions problem), the researcher performs statistical inference under the assumption that they observe a random sample from a large matching market. In…
The asymptotic solution to the problem of comparing the means of two heteroscedastic populations, based on two random samples from the populations, hinges on the pivot underpinning the construction of the confidence interval and the test…
A classical approach for approximating expectations of functions w.r.t. partially known distributions is to compute the average of function values along a trajectory of a Metropolis-Hastings (MH) Markov chain. A key part in the MH algorithm…
Symmetry is a cornerstone of much of mathematics, and many probability distributions possess symmetries characterized by their invariance to a collection of group actions. Thus, many mathematical and statistical methods rely on such…
This paper faces a central theme in applied statistics and information science, which is the assessment of the stochastic structure of rank-size laws in text analysis. We consider the words in a corpus by ranking them on the basis of their…
For integers $n\geq r$, we treat the $r$th largest of a sample of size $n$ as an $\mathbb{R}^\infty$-valued stochastic process in $r$ which we denote $\mathbf{M}^{(r)}$. We show that the sequence regarded in this way satisfies the Markov…
The most common way to sample from a probability distribution is to use Monte-Carlo methods. For distributions on a continuous state space, one can find diffusions with the target distribution as equilibrium measure, so that the state of…
It is common, when dealing with quantum processes involving a subsystem of a much larger composite closed system, to treat them as effectively memory-less (Markovian). While open systems theory tells us that non-Markovian processes should…
This paper introduces two new families of non-parametric tests of goodness-of-fit on the compact classical groups. One of them is a family of tests for the eigenvalue distribution induced by the uniform distribution, which is consistent…
A key feature of a sequential study is that the actual sample size is a random variable that typically depends on the outcomes collected. While hypothesis testing theory for sequential designs is well established, parameter and precision…
Given two random variables taking values in a bounded interval, we study whether one dominates the other in higher-order stochastic dominance depends on the reference interval in the model setting. We obtain two results. First, the…
Many machine learning applications require operating on a spatially distributed dataset. Despite technological advances, privacy considerations and communication constraints may prevent gathering the entire dataset in a central unit. In…
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…
Perfect sampling is a technique that uses coupling arguments to provide a sample from the stationary distribution of a Markov chain in a finite time without ever computing the distribution. This technique is very efficient if all the events…
Gibbs sampling repeatedly samples from the conditional distribution of one variable, x_i, given other variables, either choosing i randomly, or updating sequentially using some systematic or random order. When x_i is discrete, a Gibbs…
In the design and analysis of political redistricting maps, it is often useful to be able to sample from the space of all partitions of the graph of census blocks into connected subgraphs of equal population. There are influential Markov…
This paper is concerned with the problem of comparing the population means of two groups of independent observations. An approximate randomization test procedure based on the test statistic of Chen and Qin (2010) is proposed. The asymptotic…
We consider finite-state time-nonhomogeneous Markov chains where the probability of moving from state $i$ to state $j\neq i$ at time $n$ is $G(i,j)/n^\zeta$ for a ``generator'' matrix $G$ and strength parameter $\zeta>0$. In these chains,…
We investigate the equilibration of a small isolated quantum system by means of its matrix of asymptotic transition probabilities in a preferential basis. The trace of this matrix is shown to measure the degree of equilibration of the…