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

Jackknife Empirical Likelihood Ratio Test for Cauchy Distribution 考奇分布的积弱经验似然比检验

arXiv - STAT - Statistics Theory Pub Date : 2024-09-09 DOI: arxiv-2409.05764

Avhad Ganesh Vishnu, Ananya Lahiri, Sudheesh K. Kattumannil

引用次数: 0

Parameter estimation for fractional stochastic heat equations : Berry-Esséen bounds in CLTs 分数随机热方程的参数估计：CLT中的贝里-埃森边界

arXiv - STAT - Statistics Theory Pub Date : 2024-09-09 DOI: arxiv-2409.05416

Soukaina Douissi, Fatimah Alshahrani

引用次数: 0

On integer partitions and the Wilcoxon rank-sum statistic 关于整数分区和威尔科克森秩和统计量

arXiv - STAT - Statistics Theory Pub Date : 2024-09-09 DOI: arxiv-2409.05741

Andrew V. Sills

引用次数: 0

Empirical Bernstein in smooth Banach spaces 光滑巴拿赫空间中的经验伯恩斯坦

arXiv - STAT - Statistics Theory Pub Date : 2024-09-09 DOI: arxiv-2409.06060

Diego Martinez-Taboada, Aaditya Ramdas

引用次数: 0

Markov Chain Variance Estimation: A Stochastic Approximation Approach 马尔可夫链方差估计：随机逼近法

arXiv - STAT - Statistics Theory Pub Date : 2024-09-09 DOI: arxiv-2409.05733

Shubhada Agrawal, Prashanth L. A., Siva Theja Maguluri

{"title":"Markov Chain Variance Estimation: A Stochastic Approximation Approach","authors":"Shubhada Agrawal, Prashanth L. A., Siva Theja Maguluri","doi":"arxiv-2409.05733","DOIUrl":"https://doi.org/arxiv-2409.05733","url":null,"abstract":"We consider the problem of estimating the asymptotic variance of a function\u0000defined on a Markov chain, an important step for statistical inference of the\u0000stationary mean. We design the first recursive estimator that requires $O(1)$\u0000computation at each step, does not require storing any historical samples or\u0000any prior knowledge of run-length, and has optimal $O(frac{1}{n})$ rate of\u0000convergence for the mean-squared error (MSE) with provable finite sample\u0000guarantees. Here, $n$ refers to the total number of samples generated. The\u0000previously best-known rate of convergence in MSE was $O(frac{log n}{n})$,\u0000achieved by jackknifed estimators, which also do not enjoy these other\u0000desirable properties. Our estimator is based on linear stochastic approximation\u0000of an equivalent formulation of the asymptotic variance in terms of the\u0000solution of the Poisson equation. We generalize our estimator in several directions, including estimating the\u0000covariance matrix for vector-valued functions, estimating the stationary\u0000variance of a Markov chain, and approximately estimating the asymptotic\u0000variance in settings where the state space of the underlying Markov chain is\u0000large. We also show applications of our estimator in average reward\u0000reinforcement learning (RL), where we work with asymptotic variance as a risk\u0000measure to model safety-critical applications. We design a temporal-difference\u0000type algorithm tailored for policy evaluation in this context. We consider both\u0000the tabular and linear function approximation settings. Our work paves the way\u0000for developing actor-critic style algorithms for variance-constrained RL.","PeriodicalId":501379,"journal":{"name":"arXiv - STAT - Statistics Theory","volume":"8 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142192980","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

Empirical likelihood for generalized smoothly trimmed mean 广义平滑修剪均值的经验似然法

arXiv - STAT - Statistics Theory Pub Date : 2024-09-09 DOI: arxiv-2409.05631

Elina Kresse, Emils Silins, Janis Valeinis

引用次数: 0

Efficient estimation with incomplete data via generalised ANOVA decomposition 通过广义方差分解对不完整数据进行高效估计

arXiv - STAT - Statistics Theory Pub Date : 2024-09-09 DOI: arxiv-2409.05729

Thomas B. Berrett

{"title":"Efficient estimation with incomplete data via generalised ANOVA decomposition","authors":"Thomas B. Berrett","doi":"arxiv-2409.05729","DOIUrl":"https://doi.org/arxiv-2409.05729","url":null,"abstract":"We study the efficient estimation of a class of mean functionals in settings\u0000where a complete multivariate dataset is complemented by additional datasets\u0000recording subsets of the variables of interest. These datasets are allowed to\u0000have a general, in particular non-monotonic, structure. Our main contribution\u0000is to characterise the asymptotic minimal mean squared error for these problems\u0000and to introduce an estimator whose risk approximately matches this lower\u0000bound. We show that the efficient rescaled variance can be expressed as the\u0000minimal value of a quadratic optimisation problem over a function space, thus\u0000establishing a fundamental link between these estimation problems and the\u0000theory of generalised ANOVA decompositions. Our estimation procedure uses\u0000iterated nonparametric regression to mimic an approximate influence function\u0000derived through gradient descent. We prove that this estimator is approximately\u0000normally distributed, provide an estimator of its variance and thus develop\u0000confidence intervals of asymptotically minimal width. Finally we study a more\u0000direct estimator, which can be seen as a U-statistic with a data-dependent\u0000kernel, showing that it is also efficient under stronger regularity conditions.","PeriodicalId":501379,"journal":{"name":"arXiv - STAT - Statistics Theory","volume":"396 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142192590","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

Statistical Mechanics of Min-Max Problems 最小-最大问题的统计力学

arXiv - STAT - Statistics Theory Pub Date : 2024-09-09 DOI: arxiv-2409.06053

Yuma Ichikawa, Koji Hukushima

引用次数: 0

Common or specific source, features or scores; it is all a matter of information 共同或特定来源、特征或分数；这都是信息问题

arXiv - STAT - Statistics Theory Pub Date : 2024-09-09 DOI: arxiv-2409.05403

Aafko Boonstra, Ronald Meester, Klaas Slooten

{"title":"Common or specific source, features or scores; it is all a matter of information","authors":"Aafko Boonstra, Ronald Meester, Klaas Slooten","doi":"arxiv-2409.05403","DOIUrl":"https://doi.org/arxiv-2409.05403","url":null,"abstract":"We show that the incorporation of any new piece of information allows for\u0000improved decision making in the sense that the expected costs of an optimal\u0000decision decrease (or, in boundary cases where no or not enough new information\u0000is incorporated, stays the same) whenever this is done by the appropriate\u0000update of the probabilities of the hypotheses. Versions of this result have\u0000been stated before. However, previous proofs rely on auxiliary constructions\u0000with proper scoring rules. We, instead, offer a direct and completely general\u0000proof by considering elementary properties of likelihood ratios only. We do\u0000point out the relation to proper scoring rules. We apply our results to make a\u0000contribution to the debates about the use of score based/feature based and\u0000common/specific source likelihood ratios. In the literature these are often\u0000presented as different ``LR-systems''. We argue that deciding which LR to\u0000compute is simply a matter of the available information. There is no such thing\u0000as different ``LR-systems'', there are only differences in the available\u0000information. In particular, despite claims to the contrary, scores can very\u0000well be used in forensic practice and we illustrate this with an extensive\u0000example in DNA kinship context.","PeriodicalId":501379,"journal":{"name":"arXiv - STAT - Statistics Theory","volume":"58 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142192985","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

A Continuous Generalization of Hypothesis Testing 假设检验的连续一般化

arXiv - STAT - Statistics Theory Pub Date : 2024-09-09 DOI: arxiv-2409.05654

Nick W. Koning

引用次数: 0