TY - JOUR
AU - Withers, Christopher S.
AU - Nadarajah, Saralees
PY - 2008/01/01
Y2 - 2022/05/17
TI - Edgeworth and Cornish Fisher expansions and confidence intervals for the distribution, density and
JF - Statistica
JA - Stat
VL - 68
IS - 3/4
SE - Articles
DO - 10.6092/issn.1973-2201/3535
UR - https://rivista-statistica.unibo.it/article/view/3535
SP - 281-301
AB - We show that kernel density estimates of bandwidth h=h(n)→0 satisfy the Cornish-Fisher assumption with parameter m=nh. This allows Cornish-Fisher expansions about the normal for standardized and Studentized kernel density estimates. The expansions given are formal and the conditions for existence/validity are not explored. The expansions lead to first order confidence intervals (CIs) of level 1−ω +O(n−β), where β =p/(2p+ 2) for one-sided CIs and β = p/(p+1) for two-sided CIs, where p is the order of the kernel used. The second order one- and two-sided CIs are given with β =2p/(2p+3) and β =2p/(p+2). We show how to choose the bandwidth for asymptotic optimality.
ER -