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

Blog — PlanetScale
Blog — PlanetScale
博客园 - 司徒正美
Vercel News
Vercel News
F
Fortinet All Blogs
月光博客
月光博客
G
Google Developers Blog
博客园 - Franky
GbyAI
GbyAI
The Cloudflare Blog
I
InfoQ
雷峰网
雷峰网
WordPress大学
WordPress大学
罗磊的独立博客
大猫的无限游戏
大猫的无限游戏
T
The Blog of Author Tim Ferriss
Apple Machine Learning Research
Apple Machine Learning Research
博客园 - 聂微东
小众软件
小众软件
腾讯CDC
B
Blog
量子位
V
V2EX
S
SegmentFault 最新的问题
Google DeepMind News
Google DeepMind News

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
On a family of test statistics for discretely observed di...
Alessandro De Gregorio, Stefano Iacus · 2011-11-11 · via math.ST updates on arXiv.org

We consider parametric hypotheses testing for multidimensional ergodic diffusion processes observed at discrete time. We propose a family of test statistics, related to the so called $φ$-divergence measures. By taking into account the quasi-likelihood approach developed for studying the stochastic differential equations, it is proved that the tests in this family are all asymptotically distribution free. In other words, our test statistics weakly converge to the chi squared distribution. Furthermore, our test statistic is compared with the quasi likelihood ratio test. In the case of contiguous alternatives, it is also possible to study in detail the power function of the tests. Although all the tests in this family are asymptotically equivalent, we show by Monte Carlo analysis that, in the small sample case, the performance of the test strictly depends on the choice of the function $φ$. Furthermore, in this framework, the simulations show that there are not uniformly most powerful tests.