We propose new goodness-of-fit tests for the Poisson distribution. The testing procedure entails fitting a weighted Poisson distribution, which has the Poisson as a special case, to observed data. Based on sample data, we calculate an empirical weight function which is compared to its theoretical counterpart under the Poisson assumption. Weighted Lp distances between these empirical and theoretical functions are proposed as test statistics and closed form expressions are derived for L1, L2 and L1 distances. A Monte Carlo study is included in which the newly proposed tests are shown to be powerful when compared to existing tests, especially in the case of overdispersed alternatives. We demonstrate the use of the tests with two practical examples.
The edges in networks are not only binary, either present or absent, but also take weighted values in many scenarios (e.g., the number of emails between two users). The covariate-$p_0$ model has been proposed to model binary directed networks with the degree heterogeneity and covariates. However, it may cause information loss when it is applied in weighted networks. In this paper, we propose to use the Poisson distribution to model weighted directed networks, which admits the sparsity of networks, the degree heterogeneity and the homophily caused by covariates of nodes. We call it the \emph{ne…
University of Washington（华盛顿大学）；Google Inc（谷歌公司）；University of Wisconsin-Madison（威斯康星大学麦迪逊分校）；Fred Hutchinson Cancer Research Center（弗雷德·哈钦森癌症研究中心）
This paper investigates the theoretical and empirical performance of Fisher-Pitman-type permutation tests for assessing the equality of unknown Poisson mixture distributions. Building on nonparametric maximum likelihood estimators (NPMLEs) of the mixing distribution, these tests are theoretically shown to be able to adapt to complicated unspecified structures of count data and also consistent against their corresponding ANOVA-type alternatives; the latter is a result in parallel to classic claims made by Robinson (Robinson, 1973). The studied methods are then applied to a single-cell RNA-seq d…
Today, generalized linear mixed models are broadly used in many fields. However, the development of tools for performing simultaneous inference has been largely neglected in this domain. A framework for joint inference is indispensable to carry out statistically valid multiple comparisons of parameters of interest between all or several clusters. We therefore develop simultaneous confidence intervals and multiple testing procedures for empirical best predictors under generalized linear mixed models. In addition, we implement our methodology to study widely employed examples of mixed models, th…
In this paper, I propose a new class of Zero-Inflated Poisson models into the family of Cluster Weighted Models (CWMs) called Zero-Inflated Poisson CWMs (ZIPCWM). ZIPCWM extends Poisson cluster weighted models and other mixture models. I propose an Expectation-Maximization (EM) algorithm via an iteratively reweighted least squares for the model. I theoretically and analytically investigate the identifiability of the proposed model through an extensive simulation study. Parameter recovery, classification assessment, and performance of different information criteria are investigated through broa…
We consider the problem of the estimation of the mean function of an inhomogeneous Poisson process when its intensity function is periodic. For the mean integrated squared error (MISE) there is a classical lower bound for all estimators and the empirical mean function attains that lower bound, thus it is asymptotically efficient. Following the ideas of the work by Golubev and Levit, we compare asymptotically efficient estimators and propose an estimator which is second order asymptotically efficient. Second order efficiency is done over Sobolev ellipsoids, following the idea of Pinsker.
A Revisit to Point Estimation Through the Empirical Bayes Method: The Case of Binomial Distribution with Beta Prior and Extension to Poisson Distribution
Ho Chi Minh City University of Technology（胡志明市理工大学）；Vietnam National University Ho Chi Minh City（越南国立大学胡志明市分校）；Ton Duc Thang University（崇正大学）
