Related papers: An Exponential Inequality for U-Statistics under M…
We prove a convergence theorem for U-statistics of degree two, where the data dimension $d$ is allowed to scale with sample size $n$. We find that the limiting distribution of a U-statistic undergoes a phase transition from the…
This paper addresses differential inference in time-varying parametric probabilistic models, like graphical models with changing structures. Instead of estimating a high-dimensional model at each time point and estimating changes later, we…
This work studies the large sample properties of the posterior-based inference in the curved exponential family under increasing dimension. The curved structure arises from the imposition of various restrictions on the model, such as moment…
In this paper we consider the statistical inference of the unknown parameter of an exponential distribution based on the time truncated data. The time truncated data occurs quite often in the reliability analysis for type-I or hybrid…
Under some mild regularity on the normalizing sequence, we obtain necessary and sufficient conditions for the Strong Law of Large Numbers for (symmetrized) U-statistics. We also obtain nasc's for the a.s. convergence of series of an…
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…
A new characterization of the exponential distribution is obtained. It is based on an equation involving randomly shifted (translated) order statistics. No specific distribution is assumed for the shift random variables. The proof uses a…
Motivated by challenges on studying a new correlation measurement being popularized in evaluating online ranking algorithms' performance, this manuscript explores the validity of uncertainty assessment for weighted U-statistics. Without any…
In the setting of dominated statistical models, we provide conditions yielding strong continuity of the posterior distribution with respect to the observed data. We show some applications, with special focus on exponential models.
The asymptotic equivalence of canonical and microcanonical ensembles is a central concept in statistical physics, with important consequences for both theoretical research and practical applications. However, this property breaks down under…
The problem of measuring conditional dependence between two random phenomena arises when a third one (a confounder) has a potential influence on the amount of information between them. A typical issue in this challenging problem is the…
We examine the time variation of a previously-uninvestigated fundamental dimensionless constant. Constraints are placed on this time variation using historical measurements. A model is presented for the time variation, and it is shown to…
In data science, one is often confronted with a time series representing measurements of some quantity of interest. Usually, as a first step, features of the time series need to be extracted. These are numerical quantities that aim to…
Genetic data are frequently categorical and have complex dependence structures that are not always well understood. For this reason, clustering and classification based on genetic data, while highly relevant, are challenging statistical…
We analyze a class of models for unequal crossover (UC) of sequences containing sections with repeated units that may differ in length. In these, the probability of an `imperfect' alignment, in which the shorter sequence has d units without…
We introduce a family of coefficients based on U-statistics that generalize the notion of correlation and explore their properties in the large dimensional multivariate case, showing that in the null case of uncorrelated variables, the…
We consider the problem of testing a null hypothesis defined by equality and inequality constraints on a statistical parameter. Testing such hypotheses can be challenging because the number of relevant constraints may be on the same order…
We deduce in this paper the sufficient conditions for weak convergence of centered and normed deviation of the u-statistics with values in the space of the real valued continuous function defined on some compact metric space. We obtain also…
U-statistics are widely used in fields such as economics, machine learning, and statistics. However, while they enjoy desirable statistical properties, they have an obvious drawback in that the computation becomes impractical as the data…
We study deviation of U-statistics when samples have heavy-tailed distribution so the kernel of the U-statistic does not have bounded exponential moments at any positive point. We obtain an exponential upper bound for the tail of the…