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Let $X_1,X_2,...,X_n$ be a sequence of independent or locally dependent random variables taking values in $\mathbb{Z}_+$. In this paper, we derive sharp bounds, via a new probabilistic method, for the total variation distance between the…
Working from a Poisson-Gaussian noise model, a multi-sample extension of the Photon Counting Histogram Expectation Maximization (PCH-EM) algorithm is derived as a general-purpose alternative to the Photon Transfer (PT) method. This…
Consider a situation of analyzing high-dimensional count data containing an excess of near-zero counts with a small number of moderate or large counts. Assuming that the observations are modeled by a Poisson distribution, we are interested…
Logistic regression is a standard method in multivariate analysis for binary outcome data in epidemiological and clinical studies; however, the resultant odds-ratio estimates fail to provide directly interpretable effect measures. The…
The C statistic is a widely used likelihood-ratio statistic for model fitting and goodness-of-fit assessments with Poisson data in high-energy physics and astrophysics. Although it enjoys convenient asymptotic properties, the statistic is…
The 'standard' confidence interval for a Poisson parameter is only one of a number of estimation intervals based on the chi-square distribution that may be used in the estimation of the mean or mean rate for a Poisson model. Other…
The Dirichlet-multinomial (DM) distribution plays a fundamental role in modern statistical methodology development and application. Recently, the DM distribution and its variants have been used extensively to model multivariate count data…
This paper proposes a computationally efficient Bayesian factor model for multiple grouped count data. Adopting the link function approach, the proposed model can capture the association within and between the at-risk probabilities and…
We propose a new methodology to detect zero-inflation and overdispersion based on the comparison of the expected sample extremes among convexly ordered distributions. The method is very flexible and includes tests for the proportion of…
Nested-error regression models are widely used for analyzing clustered data. For example, they are often applied to two-stage sample surveys, and in biology and econometrics. Prediction is usually the main goal of such analyses, and…
Exact expressions are given for the distribution function of the ratio of a weighted sum of independent chi-squared variables to a single chi-square variable, scaled appropriately. This distribution is the generalization of the classical F…
We establish the convergence rates and asymptotic distributions of the common break change-point estimators, obtained by least squares and maximum likelihood in panel data models and compare their asymptotic variances. Our model assumptions…
The $\Delta_3(L)$ statistic of Random Matrix Theory is defined as the average of a set of random numbers $\{\delta\}$, derived from a spectrum. The distribution $p(\delta)$ of these random numbers is used as the basis of a maximum…
Data which lie in the space $\mathcal{P}_{m\,}$, of $m \times m$ symmetric positive definite matrices, (sometimes called tensor data), play a fundamental role in applications including medical imaging, computer vision, and radar signal…
An expectation-based scan statistic is proposed for the prospective monitoring of spatio-temporal count data with an excess of zeros. The method, which is based on an outbreak model for the zero-inflated Poisson distribution, is shown to be…
We study the problem of high-dimensional sparse mean estimation in the presence of an $\epsilon$-fraction of adversarial outliers. Prior work obtained sample and computationally efficient algorithms for this task for identity-covariance…
This paper formulates a penalized empirical likelihood (PEL) method for inference on the population mean when the dimension of the observations may grow faster than the sample size. Asymptotic distributions of the PEL ratio statistic is…
The present study proposes incorporating non-parametric knowledge into the diffusion least-mean-squares algorithm in the framework of a maximum a posteriori (MAP) estimation. The proposed algorithm leads to a robust estimation of an unknown…
The goal of subsampling is to select an informative subset of all observations, when using the full data for statistical analysis is not viable. We construct locally $ D $-optimal subsampling designs under a Poisson regression model with a…
The robust Poisson method is becoming increasingly popular when estimating the association of exposures with a binary outcome. Unlike the logistic regression model, the robust Poisson method yields results that can be interpreted as risk or…