Hölder norm test statistics for epidemic change

Estimating a Changed Segment in a Sample

“…Finally, applying Assumption (A) to the signed measure d s,h n − d * n , recalling that d * n = O Pr (n −1/2 ) and noting that by (8), (12), r * −1 n γ n n −1/2 tends to 0, we complete the proof of Claim 3.…”

“…, X n,n be a triangular array of independent random elements in E. There exist s * n and t * n such that for 1 ≤ i ≤ ns * n or nt * n < i ≤ n, the X i,n 's have distribution P n , while for ns * n < i ≤ nt * n , they have distribution Q n . We refer to e.g., Avery and Henderson [1], Commenges et al [3], Račkauskas and Suquet [12,13], Yao [17] for a comprehensive review. Our aim to this model is to estimate the pair (s * n , h * n ), where h * n = t * n − s * n measures the length of the changed segment.…”

Comments on: Extensions of some classical methods in change point analysis

“…Erdős-Rényi type normalized variables also appear when one tests for epidemic alternatives (cf. Račkauskas and Suquet 2004). Again, to obtain the limit distribution of the self-normalized statistics, the rate of approximation plays an important role.…”

Testing Epidemic Changes of Infinite Dimensional Parameters

“…In [12], we study a large class of statistics obtained by discretizing Hölder norms of the partial sums process (with B = R). One important feature of Hölderian weighting is the detection of short epidemics.…”