arXiv - STAT - Statistics Theory最新文献_第5页

A model-based approach for clustering binned data 基于模型的二进制数据聚类方法

arXiv - STAT - Statistics Theory Pub Date : 2024-09-12 DOI: arxiv-2409.07738

Asael Fabian Martínez, Carlos Díaz-Avalos

引用次数: 0

Asymptotics of Stochastic Gradient Descent with Dropout Regularization in Linear Models 线性模型中随机梯度下降与放弃正则化的渐近性

arXiv - STAT - Statistics Theory Pub Date : 2024-09-11 DOI: arxiv-2409.07434

Jiaqi Li, Johannes Schmidt-Hieber, Wei Biao Wu

引用次数: 0

Gaussian Process Upper Confidence Bounds in Distributed Point Target Tracking over Wireless Sensor Networks 无线传感器网络分布式点目标跟踪中的高斯过程置信度上限

arXiv - STAT - Statistics Theory Pub Date : 2024-09-11 DOI: arxiv-2409.07652

Xingchi Liu, Lyudmila Mihaylova, Jemin George, Tien Pham

{"title":"Gaussian Process Upper Confidence Bounds in Distributed Point Target Tracking over Wireless Sensor Networks","authors":"Xingchi Liu, Lyudmila Mihaylova, Jemin George, Tien Pham","doi":"arxiv-2409.07652","DOIUrl":"https://doi.org/arxiv-2409.07652","url":null,"abstract":"Uncertainty quantification plays a key role in the development of autonomous\u0000systems, decision-making, and tracking over wireless sensor networks (WSNs).\u0000However, there is a need of providing uncertainty confidence bounds, especially\u0000for distributed machine learning-based tracking, dealing with different volumes\u0000of data collected by sensors. This paper aims to fill in this gap and proposes\u0000a distributed Gaussian process (DGP) approach for point target tracking and\u0000derives upper confidence bounds (UCBs) of the state estimates. A unique\u0000contribution of this paper includes the derived theoretical guarantees on the\u0000proposed approach and its maximum accuracy for tracking with and without\u0000clutter measurements. Particularly, the developed approaches with uncertainty\u0000bounds are generic and can provide trustworthy solutions with an increased\u0000level of reliability. A novel hybrid Bayesian filtering method is proposed to\u0000enhance the DGP approach by adopting a Poisson measurement likelihood model.\u0000The proposed approaches are validated over a WSN case study, where sensors have\u0000limited sensing ranges. Numerical results demonstrate the tracking accuracy and\u0000robustness of the proposed approaches. The derived UCBs constitute a tool for\u0000trustworthiness evaluation of DGP approaches. The simulation results reveal\u0000that the proposed UCBs successfully encompass the true target states with 88%\u0000and 42% higher probability in X and Y coordinates, respectively, when compared\u0000to the confidence interval-based method.","PeriodicalId":501379,"journal":{"name":"arXiv - STAT - Statistics Theory","volume":"396 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142192578","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Identifiability of Polynomial Models from First Principles and via a Gröbner Basis Approach 多项式模型的可识别性源自第一原理和格伯纳基础方法

arXiv - STAT - Statistics Theory Pub Date : 2024-09-11 DOI: arxiv-2409.07062

Janet D. Godolphin, James D. E. Grant

引用次数: 0

Where does the tail start? Inflection Points and Maximum Curvature as Boundaries 尾巴从哪里开始？作为边界的拐点和最大曲率

arXiv - STAT - Statistics Theory Pub Date : 2024-09-10 DOI: arxiv-2409.06308

Rafael Cabral, Maria de Iorio, Andrea Cremaschi

{"title":"Where does the tail start? Inflection Points and Maximum Curvature as Boundaries","authors":"Rafael Cabral, Maria de Iorio, Andrea Cremaschi","doi":"arxiv-2409.06308","DOIUrl":"https://doi.org/arxiv-2409.06308","url":null,"abstract":"Understanding the tail behavior of distributions is crucial in statistical\u0000theory. For instance, the tail of a distribution plays a ubiquitous role in\u0000extreme value statistics, where it is associated with the likelihood of extreme\u0000events. There are several ways to characterize the tail of a distribution based\u0000on how the tail function, $bar{F}(x) = P(X>x)$, behaves when $xtoinfty$.\u0000However, for unimodal distributions, where does the core of the distribution\u0000end and the tail begin? This paper addresses this unresolved question and\u0000explores the usage of delimiting points obtained from the derivatives of the\u0000density function of continuous random variables, namely, the inflection point\u0000and the point of maximum curvature. These points are used to delimit the bulk\u0000of the distribution from its tails. We discuss the estimation of these\u0000delimiting points and compare them with other measures associated with the tail\u0000of a distribution, such as the kurtosis and extreme quantiles. We derive the\u0000proposed delimiting points for several known distributions and show that it can\u0000be a reasonable criterion for defining the starting point of the tail of a\u0000distribution.","PeriodicalId":501379,"journal":{"name":"arXiv - STAT - Statistics Theory","volume":"58 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142192582","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Asymptotic properties of the maximum likelihood estimator for Hidden Markov Models indexed by binary trees 以二叉树为索引的隐马尔可夫模型最大似然估计器的渐近特性

arXiv - STAT - Statistics Theory Pub Date : 2024-09-10 DOI: arxiv-2409.06295

Julien WeibelIDP, CERMICS

引用次数: 0

Many-sample tests for the equality and the proportionality hypotheses between large covariance matrices 大型协方差矩阵之间的相等假设和比例假设的多样本检验

arXiv - STAT - Statistics Theory Pub Date : 2024-09-10 DOI: arxiv-2409.06296

Tianxing Mei, Chen Wang, Jianfeng Yao

引用次数: 0

Enzyme kinetic reactions as interacting particle systems: Stochastic averaging and parameter inference 作为相互作用粒子系统的酶动力学反应：随机平均和参数推断

arXiv - STAT - Statistics Theory Pub Date : 2024-09-10 DOI: arxiv-2409.06565

Arnab Ganguly, Wasiur R. KhudaBukhsh

{"title":"Enzyme kinetic reactions as interacting particle systems: Stochastic averaging and parameter inference","authors":"Arnab Ganguly, Wasiur R. KhudaBukhsh","doi":"arxiv-2409.06565","DOIUrl":"https://doi.org/arxiv-2409.06565","url":null,"abstract":"We consider a stochastic model of multistage Michaelis--Menten (MM) type\u0000enzyme kinetic reactions describing the conversion of substrate molecules to a\u0000product through several intermediate species. The high-dimensional, multiscale\u0000nature of these reaction networks presents significant computational\u0000challenges, especially in statistical estimation of reaction rates. This\u0000difficulty is amplified when direct data on system states are unavailable, and\u0000one only has access to a random sample of product formation times. To address\u0000this, we proceed in two stages. First, under certain technical assumptions akin\u0000to those made in the Quasi-steady-state approximation (QSSA) literature, we\u0000prove two asymptotic results: a stochastic averaging principle that yields a\u0000lower-dimensional model, and a functional central limit theorem that quantifies\u0000the associated fluctuations. Next, for statistical inference of the parameters\u0000of the original MM reaction network, we develop a mathematical framework\u0000involving an interacting particle system (IPS) and prove a propagation of chaos\u0000result that allows us to write a product-form likelihood function. The novelty\u0000of the IPS-based inference method is that it does not require information about\u0000the state of the system and works with only a random sample of product\u0000formation times. We provide numerical examples to illustrate the efficacy of\u0000the theoretical results.","PeriodicalId":501379,"journal":{"name":"arXiv - STAT - Statistics Theory","volume":"255 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142192589","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

On Sparsity and Sub-Gaussianity in the Johnson-Lindenstrauss Lemma 论约翰逊-林登斯特劳斯定理中的稀疏性和次高斯性

arXiv - STAT - Statistics Theory Pub Date : 2024-09-10 DOI: arxiv-2409.06275

Aurélien GarivierUMPA-ENSL, MC2, Emmanuel PilliatUMPA-ENSL

引用次数: 0

Bootstrapping Estimators based on the Block Maxima Method 基于块最大值法的引导估计器

arXiv - STAT - Statistics Theory Pub Date : 2024-09-09 DOI: arxiv-2409.05529

Axel Bücher, Torben Staud

{"title":"Bootstrapping Estimators based on the Block Maxima Method","authors":"Axel Bücher, Torben Staud","doi":"arxiv-2409.05529","DOIUrl":"https://doi.org/arxiv-2409.05529","url":null,"abstract":"The block maxima method is a standard approach for analyzing the extremal\u0000behavior of a potentially multivariate time series. It has recently been found\u0000that the classical approach based on disjoint block maxima may be universally\u0000improved by considering sliding block maxima instead. However, the asymptotic\u0000variance formula for estimators based on sliding block maxima involves an\u0000integral over the covariance of a certain family of multivariate extreme value\u0000distributions, which makes its estimation, and inference in general, an\u0000intricate problem. As an alternative, one may rely on bootstrap approximations:\u0000we show that naive block-bootstrap approaches from time series analysis are\u0000inconsistent even in i.i.d. situations, and provide a consistent alternative\u0000based on resampling circular block maxima. As a by-product, we show consistency\u0000of the classical resampling bootstrap for disjoint block maxima, and that\u0000estimators based on circular block maxima have the same asymptotic variance as\u0000their sliding block maxima counterparts. The finite sample properties are\u0000illustrated by Monte Carlo experiments, and the methods are demonstrated by a\u0000case study of precipitation extremes.","PeriodicalId":501379,"journal":{"name":"arXiv - STAT - Statistics Theory","volume":"24 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142192984","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0