arXiv - MATH - Statistics Theory最新文献_第6页

Multivariate Unified Skew-t Distributions And Their Properties 多元统一斜-t分布及其性质

arXiv - MATH - Statistics Theory Pub Date : 2023-11-30 DOI: arxiv-2311.18294

Kesen Wang, Maicon J. Karling, Reinaldo B. Arellano-Valle, Marc G. Genton

引用次数: 0

Bayesian nonparametric inference in PDE models: asymptotic theory and implementation PDE模型中的贝叶斯非参数推理:渐近理论与实现

arXiv - MATH - Statistics Theory Pub Date : 2023-11-30 DOI: arxiv-2311.18322

Matteo Giordano

引用次数: 0

Wasserstein GANs are Minimax Optimal Distribution Estimators Wasserstein gan是极大极小最优分布估计

arXiv - MATH - Statistics Theory Pub Date : 2023-11-30 DOI: arxiv-2311.18613

Arthur Stéphanovitch, Eddie Aamari, Clément Levrard

{"title":"Wasserstein GANs are Minimax Optimal Distribution Estimators","authors":"Arthur Stéphanovitch, Eddie Aamari, Clément Levrard","doi":"arxiv-2311.18613","DOIUrl":"https://doi.org/arxiv-2311.18613","url":null,"abstract":"We provide non asymptotic rates of convergence of the Wasserstein Generative\u0000Adversarial networks (WGAN) estimator. We build neural networks classes\u0000representing the generators and discriminators which yield a GAN that achieves\u0000the minimax optimal rate for estimating a certain probability measure $mu$\u0000with support in $mathbb{R}^p$. The probability $mu$ is considered to be the\u0000push forward of the Lebesgue measure on the $d$-dimensional torus\u0000$mathbb{T}^d$ by a map $g^star:mathbb{T}^drightarrow mathbb{R}^p$ of\u0000smoothness $beta+1$. Measuring the error with the $gamma$-H\"older Integral\u0000Probability Metric (IPM), we obtain up to logarithmic factors, the minimax\u0000optimal rate $O(n^{-frac{beta+gamma}{2beta +d}}vee n^{-frac{1}{2}})$\u0000where $n$ is the sample size, $beta$ determines the smoothness of the target\u0000measure $mu$, $gamma$ is the smoothness of the IPM ($gamma=1$ is the\u0000Wasserstein case) and $dleq p$ is the intrinsic dimension of $mu$. In the\u0000process, we derive a sharp interpolation inequality between H\"older IPMs. This\u0000novel result of theory of functions spaces generalizes classical interpolation\u0000inequalities to the case where the measures involved have densities on\u0000different manifolds.","PeriodicalId":501330,"journal":{"name":"arXiv - MATH - Statistics Theory","volume":"90 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138521286","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

An analysis of multivariate measures of skewness and kurtosis of skew-elliptical distributions 偏椭圆分布的偏度和峰度的多变量测量分析

arXiv - MATH - Statistics Theory Pub Date : 2023-11-30 DOI: arxiv-2311.18176

Baishuai Zuo, Narayanaswamy Balakrishnan, Chuancun Yin

引用次数: 0

Perturbation-based Analysis of Compositional Data 基于微扰的成分数据分析

arXiv - MATH - Statistics Theory Pub Date : 2023-11-30 DOI: arxiv-2311.18501

Anton Rask Lundborg, Niklas Pfister

{"title":"Perturbation-based Analysis of Compositional Data","authors":"Anton Rask Lundborg, Niklas Pfister","doi":"arxiv-2311.18501","DOIUrl":"https://doi.org/arxiv-2311.18501","url":null,"abstract":"Existing statistical methods for compositional data analysis are inadequate\u0000for many modern applications for two reasons. First, modern compositional\u0000datasets, for example in microbiome research, display traits such as\u0000high-dimensionality and sparsity that are poorly modelled with traditional\u0000approaches. Second, assessing -- in an unbiased way -- how summary statistics\u0000of a composition (e.g., racial diversity) affect a response variable is not\u0000straightforward. In this work, we propose a framework based on hypothetical\u0000data perturbations that addresses both issues. Unlike existing methods for\u0000compositional data, we do not transform the data and instead use perturbations\u0000to define interpretable statistical functionals on the compositions themselves,\u0000which we call average perturbation effects. These average perturbation effects,\u0000which can be employed in many applications, naturally account for confounding\u0000that biases frequently used marginal dependence analyses. We show how average\u0000perturbation effects can be estimated efficiently by deriving a\u0000perturbation-dependent reparametrization and applying semiparametric estimation\u0000techniques. We analyze the proposed estimators empirically on simulated data\u0000and demonstrate advantages over existing techniques on US census and microbiome\u0000data. For all proposed estimators, we provide confidence intervals with uniform\u0000asymptotic coverage guarantees.","PeriodicalId":501330,"journal":{"name":"arXiv - MATH - Statistics Theory","volume":"86 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138521320","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

Global Convergence of Online Identification for Mixed Linear Regression 混合线性回归在线辨识的全局收敛性

arXiv - MATH - Statistics Theory Pub Date : 2023-11-30 DOI: arxiv-2311.18506

Yujing Liu, Zhixin Liu, Lei Guo

{"title":"Global Convergence of Online Identification for Mixed Linear Regression","authors":"Yujing Liu, Zhixin Liu, Lei Guo","doi":"arxiv-2311.18506","DOIUrl":"https://doi.org/arxiv-2311.18506","url":null,"abstract":"Mixed linear regression (MLR) is a powerful model for characterizing\u0000nonlinear relationships by utilizing a mixture of linear regression sub-models.\u0000The identification of MLR is a fundamental problem, where most of the existing\u0000results focus on offline algorithms, rely on independent and identically\u0000distributed (i.i.d) data assumptions, and provide local convergence results\u0000only. This paper investigates the online identification and data clustering\u0000problems for two basic classes of MLRs, by introducing two corresponding new\u0000online identification algorithms based on the expectation-maximization (EM)\u0000principle. It is shown that both algorithms will converge globally without\u0000resorting to the traditional i.i.d data assumptions. The main challenge in our\u0000investigation lies in the fact that the gradient of the maximum likelihood\u0000function does not have a unique zero, and a key step in our analysis is to\u0000establish the stability of the corresponding differential equation in order to\u0000apply the celebrated Ljung's ODE method. It is also shown that the\u0000within-cluster error and the probability that the new data is categorized into\u0000the correct cluster are asymptotically the same as those in the case of known\u0000parameters. Finally, numerical simulations are provided to verify the\u0000effectiveness of our online algorithms.","PeriodicalId":501330,"journal":{"name":"arXiv - MATH - Statistics Theory","volume":"84 5","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138521326","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

The Functional Average Treatment Effect 功能平均治疗效果

arXiv - MATH - Statistics Theory Pub Date : 2023-11-30 DOI: arxiv-2312.00219

Shane Sparkes, Erika Garcia, Lu Zhang

{"title":"The Functional Average Treatment Effect","authors":"Shane Sparkes, Erika Garcia, Lu Zhang","doi":"arxiv-2312.00219","DOIUrl":"https://doi.org/arxiv-2312.00219","url":null,"abstract":"This paper establishes the functional average as an important estimand for\u0000causal inference. The significance of the estimand lies in its robustness\u0000against traditional issues of confounding. We prove that this robustness holds\u0000even when the probability distribution of the outcome, conditional on treatment\u0000or some other vector of adjusting variables, differs almost arbitrarily from\u0000its counterfactual analogue. This paper also examines possible estimators of\u0000the functional average, including the sample mid-range, and proposes a new type\u0000of bootstrap for robust statistical inference: the Hoeffding bootstrap. After\u0000this, the paper explores a new class of variables, the $mathcal{U}$ class of\u0000variables, that simplifies the estimation of functional averages. This class of\u0000variables is also used to establish mean exchangeability in some cases and to\u0000provide the results of elementary statistical procedures, such as linear\u0000regression and the analysis of variance, with causal interpretations.\u0000Simulation evidence is provided. The methods of this paper are also applied to\u0000a National Health and Nutrition Survey data set to investigate the causal\u0000effect of exercise on the blood pressure of adult smokers.","PeriodicalId":501330,"journal":{"name":"arXiv - MATH - Statistics Theory","volume":"87 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138521318","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

Fully lifted interpolating comparisons of bilinearly indexed random processes 完全提升双线性索引随机过程的内插比较

arXiv - MATH - Statistics Theory Pub Date : 2023-11-29 DOI: arxiv-2311.18092

Mihailo Stojnic

引用次数: 0

Interaction tests with covariate-adaptive randomization 协变量自适应随机化的相互作用检验

arXiv - MATH - Statistics Theory Pub Date : 2023-11-29 DOI: arxiv-2311.17445

Likun Zhang, Wei Ma

引用次数: 0

Binary perceptrons capacity via fully lifted random duality theory 基于完全提升随机对偶理论的二元感知器容量

arXiv - MATH - Statistics Theory Pub Date : 2023-11-29 DOI: arxiv-2312.00073

Mihailo Stojnic

引用次数: 0