Related papers: On the distribution of isometric log-ratio transfo…
This paper extends Edgeworth-Cornish-Fisher expansions for the distribution and quantiles of nonparametric estimates in two ways. Firstly it allows observations to have different distributions. Secondly it allows the observations to be…
Quantitative morphologies, such as asymmetry and concentration, have long been used as an effective way to assess the distribution of galaxy starlight in large samples. Application of such quantitative indicators to other data products…
To understand how hidden information can be extracted from statistical networks, planted models in random graphs have been the focus of intensive study in recent years. In this work, we consider the detection of a planted matching, i.e., an…
The multivariate hypergeometric distribution describes sampling without replacement from a discrete population of elements divided into multiple categories. Addressing a gap in the literature, we tackle the challenge of estimating discrete…
We provide a complete asymptotic distribution theory for clustered data with a large number of independent groups, generalizing the classic laws of large numbers, uniform laws, central limit theory, and clustered covariance matrix…
Directional data require specialized probability models because of the non-Euclidean and periodic nature of their domain. When a directional variable is observed jointly with linear variables, modeling their dependence adds an additional…
We propose a Bayesian nonparametric model to infer population admixture, extending the Hierarchical Dirichlet Process to allow for correlation between loci due to Linkage Disequilibrium. Given multilocus genotype data from a sample of…
Least-squares fits are an important tool in many data analysis applications. In this paper, we review theoretical results, which are relevant for their application to data from counting experiments. Using a simple example, we illustrate the…
In this paper we extend the work of Owen (2007) by deriving a second order expansion for the slope parameter in logistic regression, when the size of the majority class is unbounded and the minority class is finite. More precisely, we…
We introduce an interpolation--regression operator for polynomial approximation on the unit sphere $\mathbb{S}^2$ from discrete samples. The approximant is a spherical polynomial of degree $r$ which interpolates the data on a prescribed…
We wish to estimate the total number of classes in a population based on sample counts, especially in the presence of high latent diversity. Drawing on probability theory that characterizes distributions on the integers by ratios of…
The use of the isoconfigurational ensemble to explore structure-dynamic correlations in supercooled liquids is examined. The statistical error of the dynamic propensity and its spatial distribution are determined. The authors present the…
Given a random text over a finite alphabet, we study the frequencies at which fixed-length words occur as subsequences. As the data size grows, the joint distribution of word counts exhibits a rich asymptotic structure. We investigate all…
Causal investigations in observational studies pose a great challenge in research where randomized trials or intervention-based studies are not feasible. We develop an information geometric causal discovery and inference framework of…
It is well known that if the power spectral density of a continuous time stationary stochastic process does not have a compact support, data sampled from that process at any uniform sampling rate leads to biased and inconsistent spectrum…
Following the development of weighted asymptotic approximation properties of matrices, we introduce the analogous uniform approximation properties (that is, study the improvability of Dirichlet's Theorem). An added feature is the use of…
We formulate a class of angular Gaussian distributions that allows different degrees of isotropy for directional random variables of arbitrary dimension. Through a series of novel reparameterization, this distribution family is indexed by…
In real world applications dealing with compositional datasets, it is easy to face the presence of structural zeros. The latter arise when, due to physical limitations, one or more variables are intrinsically zero for a subset of the…
Univariate and multivariate normal probability distributions are widely used when modeling decisions under uncertainty. Computing the performance of such models requires integrating these distributions over specific domains, which can vary…
We theoretically analyze the typical learning performance of $\ell_{1}$-regularized linear regression ($\ell_1$-LinR) for Ising model selection using the replica method from statistical mechanics. For typical random regular graphs in the…