  Infinite-order U-statistics (IOUS) has been used extensively on subbagging
ensemble learning algorithms such as random forests to quantify its
uncertainty. While normality results of IOUS have been studied extensively, its
variance estimation approaches and theoretical properties remain mostly
unexplored. Existing approaches mainly utilize the leading term dominance
property in the Hoeffding decomposition. However, such a view usually leads to
biased estimation when the kernel size is large or the sample size is small. On
the other hand, while several unbiased estimators exist in the literature,
their relationships and theoretical properties, especially the ratio
consistency, have never been studied. These limitations lead to unguaranteed
performances of constructed confidence intervals. To bridge these gaps in the
literature, we propose a new view of the Hoeffding decomposition for variance
estimation that leads to an unbiased estimator. Instead of leading term
dominance, our view utilizes the dominance of the peak region. Moreover, we
establish the connection and equivalence of our estimator with several existing
unbiased variance estimators. Theoretically, we are the first to establish the
ratio consistency of such a variance estimator, which justifies the coverage
rate of confidence intervals constructed from random forests. Numerically, we
further propose a local smoothing procedure to improve the estimator's finite
sample performance. Extensive simulation studies show that our estimators enjoy
lower bias and archive targeted coverage rates.
