Leave-p-out Cross validation

Compute risk of prediction
regression
classification
Compute the variance of $CV(m)$
where $CV(m)$ is subsample estimator of risk

Compute the variance of the extraporated estimator

2019-02-17

Empirical Process のリソース

Shorack and Wellner

van der Vaart and Wellner

Pollard

Dudley

2019-01-24

U-statistics

Variance of U-statistics
Lee p12. Sefling p183

Infinite Order U-Statistics
Frees (1989)

Helig and Nolan

Hoeffding decomposition

U 統計量をdegree がc で互いに無相関なU統計量の和に書くことができる。
この表現をHoeffding decomposition またはANOVA decomposition という。
この表現からU統計量の分散の簡易な表現が得られる。
This expression is useful even when $m$ is a functiokn of $n$

Chen and Shao (2007) derived Berry-Esseen bound for U-statistics
Shao Zhang Zhou (2016) obtained Berry-Esseen bound for studentized U-statistics
of degree 2. It is not clear to me that their result can be extended to arbitrary degree $m$