Optimal detection of general moment changes: Simultaneous mean and covariance change detection and beyond 8JDQ9FWFRK

URI	`m2://res/8JDQ9FWFRK`
Kind	preprint
Creators	Xiaokai Luo, Chenghao Xu, Haotian Xu, Carlos Misael Madrid Padilla, Daren Wang
Date	2026-09-29
Subjects	arxiv stat.ME, arxiv math.ST, arxiv stat.ML, arxiv stat.TH
Scope	border

Expressions

Date	2026-09-29
Ids	arXiv 2609.36594

The mentions of the inventory that name this resource. Each name links to the card of its inventory row.

Item	Kind	Where	Source
1JVWZWV4CB	statement	theorem 2	arxiv
Tensor-product tails	statement	lemma E.1	arxiv
416HF47B0Z	statement	theorem 1	arxiv
Consistency of the projected long-run variances	statement	lemma D.3	arxiv
Detection on an isolating seeded interval	statement	lemma A.1	arxiv
Perturbation of a maximizing direction	statement	lemma E.7	arxiv
Uniform empirical-moment and tensor CUSUM bounds	statement	theorem 7	arxiv
Size of the seeded interval collection	statement	lemma E.4	arxiv
Fourth-moment maximal bound	statement	lemma E.8	arxiv
8VKZ9PPEN1	statement	theorem 6	arxiv
9RV7MQRVTQ	statement	theorem 4	arxiv
Fitting intervals and refinement windows	statement	lemma B.1	arxiv
B087J3WX69	statement	theorem 3	arxiv
B5QW92P0PC	statement	theorem 5	arxiv
Direction accuracy for local refinement	statement	lemma B.3	arxiv
Approximating the tensor operator norm by a product net	statement	lemma E.3	arxiv
Maximal bounds near a fixed direction	statement	lemma E.9	arxiv
Fixed interval-direction concentration	statement	lemma E.2	arxiv
Simultaneous preliminary accuracy	statement	lemma B.2	arxiv
Sub-Weibull deviation under generalized-exponential $\alpha$-mixing	statement	proposition E.1	arxiv
Two-sided projected invariance principle	statement	lemma D.2	arxiv
XCRZ6PWMQB	statement	lemma E.6	arxiv
Isolating seeded interval	statement	lemma E.5	arxiv
Uniform oracle equivalence	statement	lemma D.1	arxiv
Accuracy of the estimated direction	statement	theorem 8	arxiv