Xinjia Chen
In this paper, we derive an explicit sample size formula based a mixed criterion of absolute and relative errors for estimating means of Poisson random variables.
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In this paper, we have developed a new class of sampling schemes for estimating parameters of binomial and Poisson distributions. Without any information of the unknown parameters, our sampling schemes rigorously guarantee prescribed levels of precision and confidence.
The problem of estimating the ratio of the means of a two-component Poisson mixture model is considered, when each component is subject to zero-inflation, i.e., excess zero counts. The. resulting {\it zero-inflated Poisson mixture (ZIPM) model} can be treated as a three-component Poisson mixture model with one degenerate component. The EM algorithm is applied to obtain frequentist estimators and their standard errors, the latter determined via an explicit expression for the observed information matrix. Bayes and empirical Bayes estimators also are obtained by means of conjugate priors and thei…
We present a Dempster--Shafer (DS) approach to estimating limits from Poisson counting data with nuisance parameters. Dempster--Shafer is a statistical framework that generalizes Bayesian statistics. DS calculus augments traditional probability by allowing mass to be distributed over power sets of the event space. This eliminates the Bayesian dependence on prior distributions while allowing the incorporation of prior information when it is available. We use the Poisson Dempster--Shafer model (DSM) to derive a posterior DSM for the ``Banff upper limits challenge'' three-Poisson model. The resul…
Assume that we observe a sample of size n composed of p-dimensional signals, each signal having independent entries drawn from a scaled Poisson distribution with an unknown intensity. We are interested in estimating the sum of the n unknown intensity vectors, under the assumption that most of them coincide with a given 'background' signal. The number s of p-dimensional signals different from the background signal plays the role of sparsity and the goal is to leverage this sparsity assumption in order to improve the quality of estimation as compared to the naive estimator that computes the sum …
Estimating the Partially Linear Zero-Inflated Poisson Regression Model: a Robust Approach Using a EM-like Algorithm
本文提出了一种基于EM类算法的稳健估计方法，用于解决部分线性零膨胀泊松回归模型中的异常值问题，通过模拟验证了其在有限样本中的稳健性和效率。
This paper explores large sample properties of the two-parameter $(α,θ)$ Poisson--Dirichlet Process in two contexts. In a Bayesian context of estimating an unknown probability measure, viewing this process as a natural extension of the Dirichlet process, we explore the consistency and weak convergence of the the two-parameter Poisson--Dirichlet posterior process. We also establish the weak convergence of properly centered two-parameter Poisson--Dirichlet processes for large $θ+nα.$ This latter result complements large $θ$ results for the Dirichlet process and Poisson--Dirichlet sequences, and …
Based on empirical evidence of fast mean-reverting spikes, we model electricity price processes $X+Z^β$ as the sum of a continuous Itô semimartingale $X$ and a a mean-reverting compound Poisson process $Z_t^β= \int_0^t \int_{\mathbb{R}} xe^{-β(t-s)}\underline{p}(ds,dt)$ where $\underline{p}(ds,dt)$ is Poisson random measure with intensity $λds\otimes dt$. In a first part, we investigate the estimation of $(λ,β)$ from discrete observations and establish asymptotic efficiency in various asymptotic settings. In a second part, we discuss the use of our inference results for correcting the value of…
The paper considers the problem of estimating a $p\geq2$\ dimensional mean vector of a multivariate conditionally normal distribution under quadratic loss. The problem of this type arises when estimating the parameters in a continuous time regression model with a non-Gaussian Ornstein--Uhlenbeck process driven by the mixture of a Brownian motion and a compound Poisson process.
Nonparametric estimation of the job-size distribution for an M/G/1 queue with Poisson sampling
本文提出了一种非参数估计方法，用于估计M/G/1队列中作业大小分布的累积分布函数，并探讨了其在不同分布下的收敛性和风险界。
We extend the exponential formula by Bender and Canfield (1996), which relates log-concavity and the cycle index polynomials. The extension clarifies the log-convexity relation. The proof is by noticing the property of a compound Poisson distribution together with its moment generating function. We also give a combinatorial proof of extended "log-convex part" referring Bender and Canfield's approach, where the formula by Bruijn and Erdös (1953) is additionally exploited. The combinatorial approach yields richer structural results more than log-convexity. Furthermore, we consider normal and bin…
A recurrence formula for absolute central moments of Poisson distribution is suggested.
Consider the random Dirichlet partition of the interval into $n$ fragments with parameter $θ>0$. We recall the unordered Ewens sampling formulae from finite Dirichlet partitions. As this is a key variable for estimation purposes, focus is on the number of distinct visited species in the sampling process. These are illustrated in specific cases. We use these preliminary statistical results on frequencies distribution to address the following sampling problem: what is the estimated number of species when sampling is from Dirichlet populations? The obtained results are in accordance with the ones…
In this article, we have proposed a generalized class of estimators, exponential class of estimators based on adaption of Sharma and Singh (2015) and Solanki and Singh (2013) and simple difference estimator for estimating unknown population mean in case of Poisson distributed population in simple random sampling without replacement. The expressions for mean square errors of the proposed classes of estimators are derived to the first order of approximation. It is shown that the adapted version of Solanki and Singh (2013), exponential class of estimator, is always more efficient than usual estim…
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