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

云风的 BLOG
云风的 BLOG
The GitHub Blog
The GitHub Blog
Y
Y Combinator Blog
博客园 - 三生石上(FineUI控件)
T
The Blog of Author Tim Ferriss
宝玉的分享
宝玉的分享
Hugging Face - Blog
Hugging Face - Blog
WordPress大学
WordPress大学
V
Visual Studio Blog
小众软件
小众软件
Cyber Security Advisories - MS-ISAC
Cyber Security Advisories - MS-ISAC
MongoDB | Blog
MongoDB | Blog
V
V2EX
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
博客园 - 【当耐特】
Microsoft Azure Blog
Microsoft Azure Blog
The Cloudflare Blog
H
Hackread – Cybersecurity News, Data Breaches, AI and More
freeCodeCamp Programming Tutorials: Python, JavaScript, Git & More
Engineering at Meta
Engineering at Meta
L
LangChain Blog
Martin Fowler
Martin Fowler
GbyAI
GbyAI
博客园 - 司徒正美

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
Manifold Asymptotics of Quadratic-Form-Based Inference in...
Paavo Sattler · 2019-11-06 · via math.ST updates on arXiv.org

Split-Plot or Repeated Measures Designs with multiple groups occur naturally in sciences. Their analysis is usually based on the classical Repeated Measures ANOVA. Roughly speaking, the latter can be shown to be asymptotically valid for large sample sizes $n_i$ assuming a fixed number of groups $a$ and time points $d$. However, for high-dimensional settings with $d>n_i$ this argument breaks down and statistical tests are often based on (standardized) quadratic forms. Furthermore analysis of their limit behaviour is usually based on certain assumptions on how $d$ converges to $\infty$ with respect to $n_i$. As this may be hard to argue in practice, we do not want to make such restrictions. Moreover, sometimes also the number of groups $a$ may be large compared to $d$ or $n_i$. To also have an impression about the behaviour of (standardized) quadratic forms as test statistic, we analyze their asymptotics under diverse settings on $a$, $d$ and $n_i$. In fact, we combine all kind of combinations, where they diverge or are bounded in a unified framework. Studying the limit distributions in detail, we follow Sattler and Pauly (2018) and propose an approximation to obtain critical values. The resulting test together with their approximation approach are investigated in an extensive simulation study with a focus on the exceptional asymptotic frameworks which are the main focus of this work.