惯性聚合 高效追踪和阅读你感兴趣的博客、新闻、科技资讯
阅读原文 在惯性聚合中打开

推荐订阅源

量
量子位
cs.AI updates on arXiv.org
cs.AI updates on arXiv.org
F
Fortinet All Blogs
博
博客园 - 聂微东
奇客Solidot–传递最新科技情报
奇客Solidot–传递最新科技情报
Hugging Face - Blog
Hugging Face - Blog
V
Visual Studio Blog
小众软件
小众软件
有赞技术团队
有赞技术团队
雷峰网
雷峰网
钛媒体：引领未来商业与生活新知
钛媒体：引领未来商业与生活新知
AWS News Blog
AWS News Blog
C
Cisco Blogs
美
美团技术团队
T
Threat Research - Cisco Blogs
C
CERT Recently Published Vulnerability Notes
人人都是产品经理
人人都是产品经理
宝玉的分享
宝玉的分享
Threat Intelligence Blog | Flashpoint
Threat Intelligence Blog | Flashpoint
酷 壳 – CoolShell
酷 壳 – CoolShell
Stack Overflow Blog
Stack Overflow Blog
W
WeLiveSecurity
D
DataBreaches.Net
博
博客园 - 司徒正美
Blog — PlanetScale
Blog — PlanetScale
IT之家
IT之家
云风的 BLOG
云风的 BLOG
Cyber Security Advisories - MS-ISAC
Cyber Security Advisories - MS-ISAC
Simon Willison's Weblog
Simon Willison's Weblog
Google DeepMind News
Google DeepMind News
T
The Blog of Author Tim Ferriss
Know Your Adversary
Know Your Adversary
NISL@THU
NISL@THU
OSCHINA 社区最新新闻
OSCHINA 社区最新新闻
The Cloudflare Blog
Vercel News
Vercel News
月光博客
月光博客
T
Tailwind CSS Blog
H
Help Net Security
aimingoo的专栏
aimingoo的专栏
P
Proofpoint News Feed
Application and Cybersecurity Blog
Application and Cybersecurity Blog
Spread Privacy
Spread Privacy
cs.CL updates on arXiv.org
cs.CL updates on arXiv.org
Cisco Talos Blog
Cisco Talos Blog
Microsoft Security Blog
Microsoft Security Blog
V
V2EX
WordPress大学
WordPress大学
Cyberwarzone
Cyberwarzone
Recent Announcements
Recent Announcements

math.ST updates on arXiv.org

What is Learnable in Valiant's Theory of the Learnable? Learning Perturbations to Extrapolate Your LLM Byzantine-Robust Distributed Sparse Learning Revisited The Sample Complexity of Multiple Change Point Identification under Bandit Feedback A proximal gradient algorithm for composite log-concave sampling Model-based Bootstrap of Controlled Markov Chains Approximation of Maximally Monotone Operators : A Graph Convergence Perspective Posterior Contraction Rates for Sparse Kolmogorov-Arnold Networks in Anisotropic Besov Spaces MIST: Reliable Streaming Decision Trees for Online Class-Incremental Learning via McDiarmid Bound A Spectral Framework for Closed-Form Relative Density Estimation Fast Rates for Offline Contextual Bandits with Forward-KL Regularization under Single-Policy Concentrability Higher-Order Equilibrium Tracking for EM-Compressible Online Estimation Scaling Limits of Long-Context Transformers A Note on Non-Negative $L_1$-Approximating Polynomials Susceptibilities and Patterning: A Primer on Linear Response in Bayesian Learning Linear Response Estimators for Singular Statistical Models Statistical inference with belief functions: A survey Robust stochastic first order methods in heavy-tailed noise via medoid mini-batch gradient sampling Every Feedforward Neural Network Definable in an o-Minimal Structure Has Finite Sample Complexity Adaptive auditing of AI systems with anytime-valid guarantees Locally Near Optimal Piecewise Linear Regression in High Dimensions via Difference of Max-Affine Functions Risk-Controlled Post-Processing of Decision Policies Covariate Balancing and Riesz Regression Should Be Guided by the Neyman Orthogonal Score in Debiased Machine Learning A Unified Pair-GRPO Family: From Implicit to Explicit Preference Constraints for Stable and General RL Alignment Time-Inhomogeneous Preconditioned Langevin Dynamics A Fine-Grained Understanding of Uniform Convergence for Halfspaces CITE: Anytime-Valid Statistical Inference in LLM Self-Consistency Ratio-based Loss Functions Optimal Confidence Band for Kernel Gradient Flow Estimator A renormalization-group inspired lattice-based framework for piecewise generalized linear models Direct Estimation of Schrödinger Bridge Time-Series Drifts: Finite-Sample, Asymptotic, and Adaptive Guarantees Information-theoretic Limits of Learning and Estimation Adaptivity Under Realizability Constraints: Comparing In-Context and Agentic Learning Multiscale Euclidean Network Trajectories: Second-Moment Geometry, Attribution, and Change Points Causal discovery under mean independence and linearity Perturbation is All You Need for Extrapolating Language Models Realizable Bayes-Consistency for General Metric Losses Vanishing L2 regularization for the softmax Multi Armed Bandit Imbalanced Classification under Capacity Constraints Intrinsic effective sample size for manifold-valued Markov chain Monte Carlo via kernel discrepancy On the Optimal Sample Complexity of Offline Multi-Armed Bandits with KL Regularization Extrapolation in Statistical Learning with Extreme Value Theory Adaptive Estimation and Inference in Semi-parametric Heterogeneous Clustered Multitask Learning via Neyman Orthogonality Beyond ECE: Calibrated Size Ratio, Risk Assessment, and Confidence-Weighted Metrics Self-Normalized Martingales and Uniform Regret Bounds for Linear Regression Mean Testing under Truncation beyond Gaussian Decoupled Descent: Exact Test Error Tracking Via Approximate Message Passing Hyper Input Convex Neural Networks for Shape Constrained Learning and Optimal Transport Observable Neural ODEs for Identifiable Causal Forecasting in Continuous Time Elite-Driven Support Vector Machines for Classification A Limit Theory of Foundation Models: A Mathematical Approach to Understanding Emergent Intelligence and Scaling Laws Learning Curves and Benign Overfitting of Spectral Algorithms in Large Dimensions Concave Statistical Utility Maximization Bandits via Influence-Function Gradients The Sample Complexity of Multicalibration Cover meets Robbins while Betting on Bounded Data: $\ln n$ Regret and Almost Sure $\ln\ln n$ Regret Achieving the Kesten-Stigum bound in the non-uniform hypergraph stochastic block model On two ways to use determinantal point processes for Monte Carlo integration Recovery Guarantees for Continual Learning of Dependent Tasks: Memory, Data-Dependent Regularization, and Data-Dependent Weights Structural interpretability in SVMs with truncated orthogonal polynomial kernels Cloning is as Hard as Learning for Stabilizer States Ordinary Least Squares is a Special Case of Transformer Identifiability of Potentially Degenerate Gaussian Mixture Models With Piecewise Affine Mixing NetworkNet: A Deep Neural Network Approach for Random Networks with Sparse Nodal Attributes and Complex Nodal Heterogeneity ADD for Multi-Bit Image Watermarking Cost-optimal Sequential Testing via Doubly Robust Q-learning Query Lower Bounds for Diffusion Sampling Tail-Aware Information-Theoretic Generalization for RLHF and SGLD Spatio-temporal probabilistic forecast using MMAF-guided learning The Geometry of Knowing: From Possibilistic Ignorance to Probabilistic Certainty -- A Measure-Theoretic Framework for Epistemic Convergence Generalization Properties of Score-matching Diffusion Models for Intrinsically Low-dimensional Data Conformal Policy Control Continuous-time reinforcement learning: ellipticity enables model-free value function approximation High-accuracy sampling for diffusion models and log-concave distributions Analyzing Shapley Additive Explanations to Understand Anomaly Detection Algorithm Behaviors and Their Complementarity Optimal Lower Bounds for Online Multicalibration Understanding Overparametrization in Survival Models through Interpolation Eventually LIL Regret: Almost Sure $\ln\ln T$ Regret for a sub-Gaussian Mixture on Unbounded Data Limit Theorems for Stochastic Gradient Descent in High-Dimensional Single-Layer Networks Optimal In-context Adaptivity and Distributional Robustness of Transformers Don't Pass@k: A Bayesian Framework for Large Language Model Evaluation The Good, the Bad, and the Sampled: a No-Regret Approach to Safe Online Classification GOSPA and T-GOSPA quasi-metrics for evaluation of multi-object tracking algorithms A note on the unique properties of the Kullback--Leibler divergence for sampling via gradient flows Multi-Armed Bandits With Machine Learning-Generated Surrogate Rewards Efficient compression of neural networks and datasets Out-of-Distribution Generalization of In-Context Learning: A Low-Dimensional Subspace Perspective Super-fast Rates of Convergence for Neural Network Classifiers under the Hard Margin Condition Sharp Gaussian approximations for Decentralized Federated Learning Learning Operators by Regularized Stochastic Gradient Descent with Operator-valued Kernels Smoothed Analysis of Learning from Positive Samples Statistical Impossibility and Possibility of Aligning LLMs with Human Preferences: From Condorcet Paradox to Nash Equilibrium Sharp Risk Bounds for Early-Stopping in Gaussian Linear Regression Gaussian Approximation and Multiplier Bootstrap for Stochastic Gradient Descent Copula-enhanced Vision Transformer for high myopia diagnosis through OU UWF fundus images General Frameworks for Conditional Two-Sample Testing Improved Hardness Results for Learning Intersections of Halfspaces Consistency of Lloyd's Algorithm Under Perturbations Convergence Rates for Non-Log-Concave Sampling and Log-Partition Estimation Distribution-Free Stochastic Analysis and Robust Multilevel Vector Field Anomaly Detection Efficient Parameter Estimation of Truncated Boolean Product Distributions
On point estimators for Gamma and Beta distributions
Nickos Papadatos · 2022-05-22 · via math.ST updates on arXiv.org

Let $X_1,\ldots,X_n$ be a random sample from the Gamma distribution with density $f(x)=λ^αx^{α-1}e^{-λx}/Γ(α)$, $x>0$, where both $α>0$ (the shape parameter) and $λ>0$ (the reciprocal scale parameter) are unknown. The main result shows that the uniformly minimum variance unbiased estimator (UMVUE) of the shape parameter, $α$, exists if and only if $n\geq 4$; moreover, it has finite variance if and only if $n\geq 6$. More precisely, the form of the UMVUE is given for all parametric functions $α$, $λ$, $1/α$ and $1/λ$. Furthermore, a highly efficient estimating procedure for the two-parameter Beta distribution is also given. This is based on a Stein-type covariance identity for the Beta distribution, followed by an application of the theory of $U$-statistics and the delta-method. MSC: Primary 62F10; 62F12; Secondary 62E15. Key words and phrases: unbiased estimation; Gamma distribution; Beta distribution; Ye-Chen-type closed-form estimators; asymptotic efficiency; $U$-statistics; Stein-type covariance identity; delta-method.

此内容由惯性聚合(RSS阅读器)自动聚合整理，仅供阅读参考。 原文来自 — 版权归原作者所有。