Esaim-Probability and Statistics最新文献_第8页

Cardinality estimation for random stopping sets based on Poisson point processes 基于泊松点过程的随机停止集基数估计

IF 0.4 4区数学

Esaim-Probability and Statistics Pub Date : 2021-01-01 DOI: 10.1051/PS/2021004

Nicolas Privault

引用次数: 2

Correction The probabilities of large deviations for a certain class of statistics associated with multinomial distributions 改正与多项分布有关的某一类统计数据的大偏差的概率

IF 0.4 4区数学

Esaim-Probability and Statistics Pub Date : 2021-01-01 DOI: 10.1051/ps/2021002

S. Mirakhmedov

引用次数: 0

On the curved exponential family in the Stochastic Approximation Expectation Maximization Algorithm 关于曲线指数族的随机逼近期望最大化算法

IF 0.4 4区数学

Esaim-Probability and Statistics Pub Date : 2021-01-01 DOI: 10.1051/ps/2021015

Vianney Debavelaere, S. Allassonnière

{"title":"On the curved exponential family in the Stochastic Approximation Expectation Maximization Algorithm","authors":"Vianney Debavelaere, S. Allassonnière","doi":"10.1051/ps/2021015","DOIUrl":"https://doi.org/10.1051/ps/2021015","url":null,"abstract":"The Expectation-Maximization Algorithm (EM) is a widely used method allowing to estimate the maximum likelihood of models involving latent variables. When the Expectation step cannot be computed easily, one can use stochastic versions of the EM such as the Stochastic Approximation EM. This algorithm, however, has the drawback to require the joint likelihood to belong to the curved exponential family. To overcome this problem, [16] introduced a rewriting of the model which “exponentializes” it by considering the parameter as an additional latent variable following a Normal distribution centered on the newly defined parameters and with fixed variance. The likelihood of this new exponentialized model now belongs to the curved exponential family. Although often used, there is no guarantee that the estimated mean is close to the maximum likelihood estimate of the initial model. In this paper, we quantify the error done in this estimation while considering the exponentialized model instead of the initial one. By verifying those results on an example, we see that a trade-off must be made between the speed of convergence and the tolerated error. Finally, we propose a new algorithm allowing a better estimation of the parameter in a reasonable computation time to reduce the bias.","PeriodicalId":51249,"journal":{"name":"Esaim-Probability and Statistics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85400171","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 7

New exponential dispersion models for count data: the ABM and LM classes 计数数据的新指数色散模型:ABM和LM类

IF 0.4 4区数学

Esaim-Probability and Statistics Pub Date : 2021-01-01 DOI: 10.1051/PS/2021001

S. Bar-Lev, Ad Ridder

{"title":"New exponential dispersion models for count data: the ABM and LM classes","authors":"S. Bar-Lev, Ad Ridder","doi":"10.1051/PS/2021001","DOIUrl":"https://doi.org/10.1051/PS/2021001","url":null,"abstract":"In their fundamental paper on cubic variance functions (VFs), Letac and Mora (The Annals of Statistics, 1990) presented a systematic, rigorous and comprehensive study of natural exponential families (NEFs) on the real line, their characterization through their VFs and mean value parameterization. They presented a section that for some reason has been left unnoticed. This section deals with the construction of VFs associated with NEFs of counting distributions on the set of nonnegative integers and allows to find the corresponding generating measures. As EDMs are based on NEFs, we introduce in this paper two new classes of EDMs based on their results. For these classes, which are associated with simple VFs, we derive their mean value parameterization and their associated generating measures. We also prove that they have some desirable properties. Both classes are shown to be overdispersed and zero inflated in ascending order, making them as competitive statistical models for those in use in both, statistical and actuarial modeling. To our best knowledge, the classes of counting distributions we present in this paper, have not been introduced or discussed before in the literature. To show that our classes can serve as competitive statistical models for those in use (e.g., Poisson, Negative binomial), we include a numerical example of real data. In this example, we compare the performance of our classes with relevant competitive models.","PeriodicalId":51249,"journal":{"name":"Esaim-Probability and Statistics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83775653","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 4

Law of large numbers for a two-dimensional class cover problem 二维类覆盖问题的大数定律

IF 0.4 4区数学

Esaim-Probability and Statistics Pub Date : 2021-01-01 DOI: 10.1051/ps/2021013

E. Ceyhan, J. Wierman, Pengfei Xiang

引用次数: 1

A tractable non-adaptative group testing method for non-binary measurements 一种易于处理的非二值测量的非自适应群测试方法

IF 0.4 4区数学

Esaim-Probability and Statistics Pub Date : 2020-12-16 DOI: 10.1051/ps/2022007

Émilien Joly, Bastien Mallein

引用次数: 2

Quantifying the closeness to a set of random curves via the mean marginal likelihood 通过平均边际似然来量化与一组随机曲线的接近程度

IF 0.4 4区数学

Esaim-Probability and Statistics Pub Date : 2020-12-15 DOI: 10.1051/PS/2020028

C'edric Rommel, J. Frédéric Bonnans, Baptiste Gregorutti, P. Martinon

引用次数: 2

Probabilistic representation of integration by parts formulae for some stochastic volatility models with unbounded drift 具有无界漂移的随机波动模型的部分积分公式的概率表示

IF 0.4 4区数学

Esaim-Probability and Statistics Pub Date : 2020-11-20 DOI: 10.1051/ps/2022008

Junchao Chen, N. Frikha, Houzhi Li

引用次数: 2

Convergence of a particle approximation for the quasi-stationary distribution of a diffusion process: uniform estimates in a compact soft case.p, li { white-space: pre-wrap; } 扩散过程准平稳分布的粒子逼近的收敛性:紧软情况下的均匀估计。P, li{空格:prewrap;}

IF 0.4 4区数学

Esaim-Probability and Statistics Pub Date : 2020-10-20 DOI: 10.1051/ps/2021017

Lucas Journel, Pierre Monmarch'e

引用次数: 9

Approximating quasi-stationary distributions with interacting reinforced random walks 用相互作用增强随机漫步逼近拟平稳分布

IF 0.4 4区数学

Esaim-Probability and Statistics Pub Date : 2020-10-20 DOI: 10.1051/ps/2021019

A. Budhiraja, Nicolas Fraiman, Adam Waterbury

{"title":"Approximating quasi-stationary distributions with interacting reinforced random walks","authors":"A. Budhiraja, Nicolas Fraiman, Adam Waterbury","doi":"10.1051/ps/2021019","DOIUrl":"https://doi.org/10.1051/ps/2021019","url":null,"abstract":"We propose two numerical schemes for approximating quasi-stationary distributions (QSD) of finite state Markov chains with absorbing states. Both schemes are described in terms of interacting chains where the interaction is given in terms of the total time occupation measure of all particles in the system and has the impact of reinforcing transitions, in an appropriate fashion, to states where the collection of particles has spent more time. The schemes can be viewed as combining the key features of the two basic simulation-based methods for approximating QSD originating from the works of Fleming and Viot (1979) and \u0000\u0000Aldous, Flannery and Palacios (1998), respectively. The key difference between the two schemes studied here is that in the first method one starts with $a(n)$ particles at time $0$ and number of particles stays constant over time whereas in the second method we start with one particle and at most one particle is added at each time instant in such a manner that there are $a(n)$ particles at time $n$. We prove almost sure convergence to the unique QSD and establish Central Limit Theorems for the two schemes under the key assumption that $a(n)=o(n)$. Exploratory numerical results are presented to illustrate the performance.","PeriodicalId":51249,"journal":{"name":"Esaim-Probability and Statistics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2020-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79964906","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 3