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

Convergence of opinions 意见趋同

arXiv - MATH - Statistics Theory Pub Date : 2023-12-04 DOI: arxiv-2312.02033

Vladimir Vovk

引用次数: 0

Cone Ranking for Multi-Criteria Decision Making 多标准决策的锥形排序

arXiv - MATH - Statistics Theory Pub Date : 2023-12-04 DOI: arxiv-2312.03006

Andreas H Hamel, Daniel Kostner

引用次数: 0

A unified framework for covariate adjustment under stratified randomization 分层随机化下协变量调整的统一框架

arXiv - MATH - Statistics Theory Pub Date : 2023-12-03 DOI: arxiv-2312.01266

Fuyi Tu, Wei Ma, Hanzhong Liu

{"title":"A unified framework for covariate adjustment under stratified randomization","authors":"Fuyi Tu, Wei Ma, Hanzhong Liu","doi":"arxiv-2312.01266","DOIUrl":"https://doi.org/arxiv-2312.01266","url":null,"abstract":"Randomization, as a key technique in clinical trials, can eliminate sources\u0000of bias and produce comparable treatment groups. In randomized experiments, the\u0000treatment effect is a parameter of general interest. Researchers have explored\u0000the validity of using linear models to estimate the treatment effect and\u0000perform covariate adjustment and thus improve the estimation efficiency.\u0000However, the relationship between covariates and outcomes is not necessarily\u0000linear, and is often intricate. Advances in statistical theory and related\u0000computer technology allow us to use nonparametric and machine learning methods\u0000to better estimate the relationship between covariates and outcomes and thus\u0000obtain further efficiency gains. However, theoretical studies on how to draw\u0000valid inferences when using nonparametric and machine learning methods under\u0000stratified randomization are yet to be conducted. In this paper, we discuss a\u0000unified framework for covariate adjustment and corresponding statistical\u0000inference under stratified randomization and present a detailed proof of the\u0000validity of using local linear kernel-weighted least squares regression for\u0000covariate adjustment in treatment effect estimators as a special case. In the\u0000case of high-dimensional data, we additionally propose an algorithm for\u0000statistical inference using machine learning methods under stratified\u0000randomization, which makes use of sample splitting to alleviate the\u0000requirements on the asymptotic properties of machine learning methods. Finally,\u0000we compare the performances of treatment effect estimators using different\u0000machine learning methods by considering various data generation scenarios, to\u0000guide practical research.","PeriodicalId":501330,"journal":{"name":"arXiv - MATH - Statistics Theory","volume":"83 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138521424","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 the admissibility of Horvitz-Thompson estimator for estimating causal effects under network interference 网络干扰下估计因果效应的Horvitz-Thompson估计的可容许性

arXiv - MATH - Statistics Theory Pub Date : 2023-12-02 DOI: arxiv-2312.01234

Vishesh Karwa, Edoardo M. Airoldi

引用次数: 0

Bagged Regularized $k$-Distances for Anomaly Detection 袋化正则化$k$-距离异常检测

arXiv - MATH - Statistics Theory Pub Date : 2023-12-02 DOI: arxiv-2312.01046

Yuchao Cai, Yuheng Ma, Hanfang Yang, Hanyuan Hang

{"title":"Bagged Regularized $k$-Distances for Anomaly Detection","authors":"Yuchao Cai, Yuheng Ma, Hanfang Yang, Hanyuan Hang","doi":"arxiv-2312.01046","DOIUrl":"https://doi.org/arxiv-2312.01046","url":null,"abstract":"We consider the paradigm of unsupervised anomaly detection, which involves\u0000the identification of anomalies within a dataset in the absence of labeled\u0000examples. Though distance-based methods are top-performing for unsupervised\u0000anomaly detection, they suffer heavily from the sensitivity to the choice of\u0000the number of the nearest neighbors. In this paper, we propose a new\u0000distance-based algorithm called bagged regularized $k$-distances for anomaly\u0000detection (BRDAD) converting the unsupervised anomaly detection problem into a\u0000convex optimization problem. Our BRDAD algorithm selects the weights by\u0000minimizing the surrogate risk, i.e., the finite sample bound of the empirical\u0000risk of the bagged weighted $k$-distances for density estimation (BWDDE). This\u0000approach enables us to successfully address the sensitivity challenge of the\u0000hyperparameter choice in distance-based algorithms. Moreover, when dealing with\u0000large-scale datasets, the efficiency issues can be addressed by the\u0000incorporated bagging technique in our BRDAD algorithm. On the theoretical side,\u0000we establish fast convergence rates of the AUC regret of our algorithm and\u0000demonstrate that the bagging technique significantly reduces the computational\u0000complexity. On the practical side, we conduct numerical experiments on anomaly\u0000detection benchmarks to illustrate the insensitivity of parameter selection of\u0000our algorithm compared with other state-of-the-art distance-based methods.\u0000Moreover, promising improvements are brought by applying the bagging technique\u0000in our algorithm on real-world datasets.","PeriodicalId":501330,"journal":{"name":"arXiv - MATH - Statistics Theory","volume":"88 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138521314","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

Identification and Inference for Synthetic Controls with Confounding 混杂综合控制的辨识与推理

arXiv - MATH - Statistics Theory Pub Date : 2023-12-01 DOI: arxiv-2312.00955

Guido W. Imbens, Davide Viviano

引用次数: 0

Inference on common trends in functional time series 函数时间序列中共同趋势的推断

arXiv - MATH - Statistics Theory Pub Date : 2023-12-01 DOI: arxiv-2312.00590

Morten Ørregaard Nielsen, Won-Ki Seo, Dakyung Seong

引用次数: 0

Multiple Testing of Linear Forms for Noisy Matrix Completion 噪声矩阵补全线性形式的多重检验

arXiv - MATH - Statistics Theory Pub Date : 2023-12-01 DOI: arxiv-2312.00305

Wanteng Ma, Lilun Du, Dong Xia, Ming Yuan