arXiv - STAT - Statistics Theory最新文献

Asymptotics for conformal inference 保角推理的渐近论

arXiv - STAT - Statistics Theory Pub Date : 2024-09-18 DOI: arxiv-2409.12019

Ulysse Gazin

引用次数: 0

An exponential inequality for Hilbert-valued U-statistics of i.i.d. data i.i.d. 数据的希尔伯特值 U 统计指数不等式

arXiv - STAT - Statistics Theory Pub Date : 2024-09-18 DOI: arxiv-2409.11737

Davide GiraudoIRMA

引用次数: 0

Incremental effects for continuous exposures 连续暴露的递增效应

arXiv - STAT - Statistics Theory Pub Date : 2024-09-18 DOI: arxiv-2409.11967

Kyle Schindl, Shuying Shen, Edward H. Kennedy

{"title":"Incremental effects for continuous exposures","authors":"Kyle Schindl, Shuying Shen, Edward H. Kennedy","doi":"arxiv-2409.11967","DOIUrl":"https://doi.org/arxiv-2409.11967","url":null,"abstract":"Causal inference problems often involve continuous treatments, such as dose,\u0000duration, or frequency. However, continuous exposures bring many challenges,\u0000both with identification and estimation. For example, identifying standard\u0000dose-response estimands requires that everyone has some chance of receiving any\u0000particular level of the exposure (i.e., positivity). In this work, we explore\u0000an alternative approach: rather than estimating dose-response curves, we\u0000consider stochastic interventions based on exponentially tilting the treatment\u0000distribution by some parameter $delta$, which we term an incremental effect.\u0000This increases or decreases the likelihood a unit receives a given treatment\u0000level, and crucially, does not require positivity for identification. We begin\u0000by deriving the efficient influence function and semiparametric efficiency\u0000bound for these incremental effects under continuous exposures. We then show\u0000that estimation of the incremental effect is dependent on the size of the\u0000exponential tilt, as measured by $delta$. In particular, we derive new minimax\u0000lower bounds illustrating how the best possible root mean squared error scales\u0000with an effective sample size of $n/delta$, instead of usual sample size $n$.\u0000Further, we establish new convergence rates and bounds on the bias of double\u0000machine learning-style estimators. Our novel analysis gives a better dependence\u0000on $delta$ compared to standard analyses, by using mixed supremum and $L_2$\u0000norms, instead of just $L_2$ norms from Cauchy-Schwarz bounds. Finally, we show\u0000that taking $delta to infty$ gives a new estimator of the dose-response\u0000curve at the edge of the support, and we give a detailed study of convergence\u0000rates in this regime.","PeriodicalId":501379,"journal":{"name":"arXiv - STAT - Statistics Theory","volume":"3 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142267766","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

Cyclicity Analysis of the Ornstein-Uhlenbeck Process 奥恩斯坦-乌伦贝克过程的周期性分析

arXiv - STAT - Statistics Theory Pub Date : 2024-09-18 DOI: arxiv-2409.12102

Vivek Kaushik

{"title":"Cyclicity Analysis of the Ornstein-Uhlenbeck Process","authors":"Vivek Kaushik","doi":"arxiv-2409.12102","DOIUrl":"https://doi.org/arxiv-2409.12102","url":null,"abstract":"In this thesis, we consider an $N$-dimensional Ornstein-Uhlenbeck (OU)\u0000process satisfying the linear stochastic differential equation $dmathbf x(t) =\u0000- mathbf Bmathbf x(t) dt + boldsymbol Sigma d mathbf w(t).$ Here, $mathbf\u0000B$ is a fixed $N times N$ circulant friction matrix whose eigenvalues have\u0000positive real parts, $boldsymbol Sigma$ is a fixed $N times M$ matrix. We\u0000consider a signal propagation model governed by this OU process. In this model,\u0000an underlying signal propagates throughout a network consisting of $N$ linked\u0000sensors located in space. We interpret the $n$-th component of the OU process\u0000as the measurement of the propagating effect made by the $n$-th sensor. The\u0000matrix $mathbf B$ represents the sensor network structure: if $mathbf B$ has\u0000first row $(b_1 , dots , b_N),$ where $b_1>0$ and $b_2 , dots \u0000, b_N le 0,$ then the magnitude of $b_p$ quantifies how receptive the $n$-th\u0000sensor is to activity within the $(n+p-1)$-th sensor. Finally, the $(m,n)$-th\u0000entry of the matrix $mathbf D = frac{boldsymbol Sigma boldsymbol\u0000Sigma^text T}{2}$ is the covariance of the component noises injected into the\u0000$m$-th and $n$-th sensors. For different choices of $mathbf B$ and\u0000$boldsymbol Sigma,$ we investigate whether Cyclicity Analysis enables us to\u0000recover the structure of network. Roughly speaking, Cyclicity Analysis studies\u0000the lead-lag dynamics pertaining to the components of a multivariate signal. We\u0000specifically consider an $N times N$ skew-symmetric matrix $mathbf Q,$ known\u0000as the lead matrix, in which the sign of its $(m,n)$-th entry captures the\u0000lead-lag relationship between the $m$-th and $n$-th component OU processes. We\u0000investigate whether the structure of the leading eigenvector of $mathbf Q,$\u0000the eigenvector corresponding to the largest eigenvalue of $mathbf Q$ in\u0000modulus, reflects the network structure induced by $mathbf B.$","PeriodicalId":501379,"journal":{"name":"arXiv - STAT - Statistics Theory","volume":"20 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142267762","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

Linear hypothesis testing in high-dimensional heteroscedastics via random integration 通过随机积分在高维异序中进行线性假设检验

arXiv - STAT - Statistics Theory Pub Date : 2024-09-18 DOI: arxiv-2409.12066

Mingxiang Cao, Hongwei Zhang, Kai Xu, Daojiang He

引用次数: 0

Sparse Factor Analysis for Categorical Data with the Group-Sparse Generalized Singular Value Decomposition 利用组-解析广义奇异值分解对分类数据进行稀疏因子分析

arXiv - STAT - Statistics Theory Pub Date : 2024-09-18 DOI: arxiv-2409.11789

Ju-Chi YuCAMH, Julie Le BorgneRID-AGE, CHRU Lille, Anjali KrishnanCUNY, Arnaud GloaguenCNRGH, JACOB, Cheng-Ta YangNCKU, Laura A RabinCUNY, Hervé AbdiUT Dallas, Vincent Guillemot

{"title":"Sparse Factor Analysis for Categorical Data with the Group-Sparse Generalized Singular Value Decomposition","authors":"Ju-Chi YuCAMH, Julie Le BorgneRID-AGE, CHRU Lille, Anjali KrishnanCUNY, Arnaud GloaguenCNRGH, JACOB, Cheng-Ta YangNCKU, Laura A RabinCUNY, Hervé AbdiUT Dallas, Vincent Guillemot","doi":"arxiv-2409.11789","DOIUrl":"https://doi.org/arxiv-2409.11789","url":null,"abstract":"Correspondence analysis, multiple correspondence analysis and their\u0000discriminant counterparts (i.e., discriminant simple correspondence analysis\u0000and discriminant multiple correspondence analysis) are methods of choice for\u0000analyzing multivariate categorical data. In these methods, variables are\u0000integrated into optimal components computed as linear combinations whose\u0000weights are obtained from a generalized singular value decomposition (GSVD)\u0000that integrates specific metric constraints on the rows and columns of the\u0000original data matrix. The weights of the linear combinations are, in turn, used\u0000to interpret the components, and this interpretation is facilitated when\u0000components are 1) pairwise orthogonal and 2) when the values of the weights are\u0000either large or small but not intermediate-a pattern called a simple or a\u0000sparse structure. To obtain such simple configurations, the optimization\u0000problem solved by the GSVD is extended to include new constraints that\u0000implement component orthogonality and sparse weights. Because multiple\u0000correspondence analysis represents qualitative variables by a set of binary\u0000variables, an additional group constraint is added to the optimization problem\u0000in order to sparsify the whole set representing one qualitative variable. This\u0000new algorithm-called group-sparse GSVD (gsGSVD)-integrates these constraints\u0000via an iterative projection scheme onto the intersection of subspaces where\u0000each subspace implements a specific constraint. In this paper, we expose this\u0000new algorithm and show how it can be adapted to the sparsification of simple\u0000and multiple correspondence analysis, and illustrate its applications with the\u0000analysis of four different data sets-each illustrating the sparsification of a\u0000particular CA-based analysis.","PeriodicalId":501379,"journal":{"name":"arXiv - STAT - Statistics Theory","volume":"6 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142267765","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

Poisson and Gamma Model Marginalisation and Marginal Likelihood calculation using Moment-generating Functions 泊松模型和伽玛模型边际化以及使用时刻生成函数计算边际似然值

arXiv - STAT - Statistics Theory Pub Date : 2024-09-17 DOI: arxiv-2409.11167

Siyang Li, David van Dyk, Maximilian Autenrieth

引用次数: 0

Edge spectra of Gaussian random symmetric matrices with correlated entries 具有相关条目的高斯随机对称矩阵的边缘谱

arXiv - STAT - Statistics Theory Pub Date : 2024-09-17 DOI: arxiv-2409.11381

Debapratim Banerjee, Soumendu Sundar Mukherjee, Dipranjan Pal

{"title":"Edge spectra of Gaussian random symmetric matrices with correlated entries","authors":"Debapratim Banerjee, Soumendu Sundar Mukherjee, Dipranjan Pal","doi":"arxiv-2409.11381","DOIUrl":"https://doi.org/arxiv-2409.11381","url":null,"abstract":"We study the largest eigenvalue of a Gaussian random symmetric matrix $X_n$,\u0000with zero-mean, unit variance entries satisfying the condition $sup_{(i, j)\u0000ne (i', j')}|mathbb{E}[X_{ij} X_{i'j'}]| = O(n^{-(1 + varepsilon)})$, where\u0000$varepsilon > 0$. It follows from Catalano et al. (2024) that the empirical\u0000spectral distribution of $n^{-1/2} X_n$ converges weakly almost surely to the\u0000standard semi-circle law. Using a F\"{u}redi-Koml'{o}s-type high moment\u0000analysis, we show that the largest eigenvalue $lambda_1(n^{-1/2} X_n)$ of\u0000$n^{-1/2} X_n$ converges almost surely to $2$. This result is essentially\u0000optimal in the sense that one cannot take $varepsilon = 0$ and still obtain an\u0000almost sure limit of $2$. We also derive Gaussian fluctuation results for the\u0000largest eigenvalue in the case where the entries have a common non-zero mean.\u0000Let $Y_n = X_n + frac{lambda}{sqrt{n}}mathbf{1} mathbf{1}^top$. When\u0000$varepsilon ge 1$ and $lambda gg n^{1/4}$, we show that [ n^{1/2}bigg(lambda_1(n^{-1/2} Y_n) - lambda - frac{1}{lambda}bigg)\u0000xrightarrow{d} sqrt{2} Z, ] where $Z$ is a standard Gaussian. On the other\u0000hand, when $0 < varepsilon < 1$, we have $mathrm{Var}(frac{1}{n}sum_{i,\u0000j}X_{ij}) = O(n^{1 - varepsilon})$. Assuming that\u0000$mathrm{Var}(frac{1}{n}sum_{i, j} X_{ij}) = sigma^2 n^{1 - varepsilon} (1\u0000+ o(1))$, if $lambda gg n^{varepsilon/4}$, then we have [ n^{varepsilon/2}bigg(lambda_1(n^{-1/2} Y_n) - lambda -\u0000frac{1}{lambda}bigg) xrightarrow{d} sigma Z. ] While the ranges of\u0000$lambda$ in these fluctuation results are certainly not optimal, a striking\u0000aspect is that different scalings are required in the two regimes $0 <\u0000varepsilon < 1$ and $varepsilon ge 1$.","PeriodicalId":501379,"journal":{"name":"arXiv - STAT - Statistics Theory","volume":"33 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142267803","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

Large Deviations Principle for Bures-Wasserstein Barycenters 布雷斯-瓦塞尔斯坦原点的大偏差原理

arXiv - STAT - Statistics Theory Pub Date : 2024-09-17 DOI: arxiv-2409.11384

Adam Quinn Jaffe, Leonardo V. Santoro

引用次数: 0

Valid Credible Ellipsoids for Linear Functionals by a Renormalized Bernstein-von Mises Theorem 通过重规范化伯恩斯坦-冯-米塞斯定理实现线性函数的有效可信椭圆形

arXiv - STAT - Statistics Theory Pub Date : 2024-09-17 DOI: arxiv-2409.10947

Gustav Rømer

引用次数: 0