arXiv - STAT - Statistics Theory最新文献_第7页

Exact exponential tail estimation for sums of independent centered random variables, under natural norming, with applications to the theory of U-statistics 自然规范下独立居中随机变量之和的精确指数尾估计，以及在 U 统计理论中的应用

arXiv - STAT - Statistics Theory Pub Date : 2024-09-08 DOI: arxiv-2409.05083

M. R. Formica, E. Ostrovsky, L. Sirota

引用次数: 0

Precise Asymptotics for Linear Mixed Models with Crossed Random Effects 具有交叉随机效应的线性混合模型的精确渐近性

arXiv - STAT - Statistics Theory Pub Date : 2024-09-08 DOI: arxiv-2409.05066

Jiming Jiang, Matt P. Wand, Swarnadip Ghosh

引用次数: 0

Privacy enhanced collaborative inference in the Cox proportional hazards model for distributed data 针对分布式数据的考克斯比例危害模型中隐私增强型协作推理

arXiv - STAT - Statistics Theory Pub Date : 2024-09-07 DOI: arxiv-2409.04716

Mengtong Hu, Xu Shi, Peter X. -K. Song

{"title":"Privacy enhanced collaborative inference in the Cox proportional hazards model for distributed data","authors":"Mengtong Hu, Xu Shi, Peter X. -K. Song","doi":"arxiv-2409.04716","DOIUrl":"https://doi.org/arxiv-2409.04716","url":null,"abstract":"Data sharing barriers are paramount challenges arising from multicenter\u0000clinical studies where multiple data sources are stored in a distributed\u0000fashion at different local study sites. Particularly in the case of\u0000time-to-event analysis when global risk sets are needed for the Cox\u0000proportional hazards model, access to a centralized database is typically\u0000necessary. Merging such data sources into a common data storage for a\u0000centralized statistical analysis requires a data use agreement, which is often\u0000time-consuming. Furthermore, the construction and distribution of risk sets to\u0000participating clinical centers for subsequent calculations may pose a risk of\u0000revealing individual-level information. We propose a new collaborative Cox\u0000model that eliminates the need for accessing the centralized database and\u0000constructing global risk sets but needs only the sharing of summary statistics\u0000with significantly smaller dimensions than risk sets. Thus, the proposed\u0000collaborative inference enjoys maximal protection of data privacy. We show\u0000theoretically and numerically that the new distributed proportional hazards\u0000model approach has little loss of statistical power when compared to the\u0000centralized method that requires merging the entire data. We present a\u0000renewable sieve method to establish large-sample properties for the proposed\u0000method. We illustrate its performance through simulation experiments and a\u0000real-world data example from patients with kidney transplantation in the Organ\u0000Procurement and Transplantation Network (OPTN) to understand the factors\u0000associated with the 5-year death-censored graft failure (DCGF) for patients who\u0000underwent kidney transplants in the US.","PeriodicalId":501379,"journal":{"name":"arXiv - STAT - Statistics Theory","volume":"33 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142192991","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

Generative Modelling via Quantile Regression 通过定量回归建立生成模型

arXiv - STAT - Statistics Theory Pub Date : 2024-09-06 DOI: arxiv-2409.04231

Johannes Schmidt-Hieber, Petr Zamolodtchikov

引用次数: 0

Improved Catoni-Type Confidence Sequences for Estimating the Mean When the Variance Is Infinite 方差无限时估计均值的改进卡托尼型置信序列

arXiv - STAT - Statistics Theory Pub Date : 2024-09-06 DOI: arxiv-2409.04198

Chengfu Wei, Jordan Stoyanov, Yiming Chen, Zijun Chen

{"title":"Improved Catoni-Type Confidence Sequences for Estimating the Mean When the Variance Is Infinite","authors":"Chengfu Wei, Jordan Stoyanov, Yiming Chen, Zijun Chen","doi":"arxiv-2409.04198","DOIUrl":"https://doi.org/arxiv-2409.04198","url":null,"abstract":"We consider a discrete time stochastic model with infinite variance and study\u0000the mean estimation problem as in Wang and Ramdas (2023). We refine the\u0000Catoni-type confidence sequence (abbr. CS) and use an idea of Bhatt et al.\u0000(2022) to achieve notable improvements of some currently existing results for\u0000such model. Specifically, for given $alpha in (0, 1]$, we assume that there is a known\u0000upper bound $nu_{alpha} > 0$ for the $(1 + alpha)$-th central moment of the\u0000population distribution that the sample follows. Our findings replicate and\u0000`optimize' results in the above references for $alpha = 1$ (i.e., in models\u0000with finite variance) and enhance the results for $alpha < 1$. Furthermore, by\u0000employing the stitching method, we derive an upper bound on the width of the CS\u0000as $mathcal{O} left(((log log t)/t)^{frac{alpha}{1+alpha}}right)$ for\u0000the shrinking rate as $t$ increases, and $mathcal{O}(left(log\u0000(1/delta)right)^{frac{alpha }{1+alpha}})$ for the growth rate as $delta$\u0000decreases. These bounds are improving upon the bounds found in Wang and Ramdas\u0000(2023). Our theoretical results are illustrated by results from a series of\u0000simulation experiments. Comparing the performance of our improved\u0000$alpha$-Catoni-type CS with the bound in the above cited paper indicates that\u0000our CS achieves tighter width.","PeriodicalId":501379,"journal":{"name":"arXiv - STAT - Statistics Theory","volume":"15 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142192992","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

Random effects estimation in a fractional diffusion model based on continuous observations 基于连续观测的分数扩散模型中的随机效应估计

arXiv - STAT - Statistics Theory Pub Date : 2024-09-06 DOI: arxiv-2409.04331

Nesrine Chebli, Hamdi Fathallah, Yousri Slaoui

{"title":"Random effects estimation in a fractional diffusion model based on continuous observations","authors":"Nesrine Chebli, Hamdi Fathallah, Yousri Slaoui","doi":"arxiv-2409.04331","DOIUrl":"https://doi.org/arxiv-2409.04331","url":null,"abstract":"The purpose of the present work is to construct estimators for the random\u0000effects in a fractional diffusion model using a hybrid estimation method where\u0000we combine parametric and nonparametric thechniques. We precisely consider $n$\u0000stochastic processes $left{X_t^j, 0leq tleq Tright}$, $j=1,ldots, n$\u0000continuously observed over the time interval $[0,T]$, where the dynamics of\u0000each process are described by fractional stochastic differential equations with\u0000drifts depending on random effects. We first construct a parametric estimator\u0000for the random effects using the techniques of maximum likelihood estimation\u0000and we study its asymptotic properties when the time horizon $T$ is\u0000sufficiently large. Then by taking into account the obtained estimator for the\u0000random effects, we build a nonparametric estimator for their common unknown\u0000density function using Bernstein polynomials approximation. Some asymptotic\u0000properties of the density estimator, such as its asymptotic bias, variance and\u0000mean integrated squared error, are studied for an infinite time horizon $T$ and\u0000a fixed sample size $n$. The asymptotic normality and the uniform convergence\u0000of the estimator are investigated for an infinite time horizon $T$, a high\u0000frequency and as the order of Bernstein polynomials is sufficiently large. Some\u0000numerical simulations are also presented to illustrate the performance of the\u0000Bernstein polynomials based estimator compared to standard Kernel estimator for\u0000the random effects density function.","PeriodicalId":501379,"journal":{"name":"arXiv - STAT - Statistics Theory","volume":"140 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142192988","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

Estimation of Proportion of Null Hypotheses Under Dependence 依赖性条件下的零假设比例估计

arXiv - STAT - Statistics Theory Pub Date : 2024-09-06 DOI: arxiv-2409.04100

Nabaneet Das

引用次数: 0

Optimal Fidelity Estimation from Binary Measurements for Discrete and Continuous Variable Systems 离散和连续可变系统二元测量的最佳保真度估计

arXiv - STAT - Statistics Theory Pub Date : 2024-09-06 DOI: arxiv-2409.04189

Omar Fawzi, Aadil Oufkir, Robert Salzmann

{"title":"Optimal Fidelity Estimation from Binary Measurements for Discrete and Continuous Variable Systems","authors":"Omar Fawzi, Aadil Oufkir, Robert Salzmann","doi":"arxiv-2409.04189","DOIUrl":"https://doi.org/arxiv-2409.04189","url":null,"abstract":"Estimating the fidelity between a desired target quantum state and an actual\u0000prepared state is essential for assessing the success of experiments. For pure\u0000target states, we use functional representations that can be measured directly\u0000and determine the number of copies of the prepared state needed for fidelity\u0000estimation. In continuous variable (CV) systems, we utilise the Wigner\u0000function, which can be measured via displaced parity measurements. We provide\u0000upper and lower bounds on the sample complexity required for fidelity\u0000estimation, considering the worst-case scenario across all possible prepared\u0000states. For target states of particular interest, such as Fock and Gaussian\u0000states, we find that this sample complexity is characterised by the $L^1$-norm\u0000of the Wigner function, a measure of Wigner negativity widely studied in the\u0000literature, in particular in resource theories of quantum computation. For\u0000discrete variable systems consisting of $n$ qubits, we explore fidelity\u0000estimation protocols using Pauli string measurements. Similarly to the CV\u0000approach, the sample complexity is shown to be characterised by the $L^1$-norm\u0000of the characteristic function of the target state for both Haar random states\u0000and stabiliser states. Furthermore, in a general black box model, we prove\u0000that, for any target state, the optimal sample complexity for fidelity\u0000estimation is characterised by the smoothed $L^1$-norm of the target state. To\u0000the best of our knowledge, this is the first time the $L^1$-norm of the Wigner\u0000function provides a lower bound on the cost of some information processing\u0000task.","PeriodicalId":501379,"journal":{"name":"arXiv - STAT - Statistics Theory","volume":"58 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142192994","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

Estimation of service value parameters for a queue with unobserved balking 具有未观察到的逡巡现象的队列的服务价值参数估计

arXiv - STAT - Statistics Theory Pub Date : 2024-09-06 DOI: arxiv-2409.04090

Daniel Podorojnyi, Liron Ravner

引用次数: 0

Approximate D-optimal design and equilibrium measure * 近似 D-最优设计和均衡度量 *

arXiv - STAT - Statistics Theory Pub Date : 2024-09-06 DOI: arxiv-2409.04058

Didier HenrionLAAS-POP, Jean Bernard LasserreLAAS-POP, TSE-R

引用次数: 0