Edgeworth and Cornish Fisher expansions and confidence intervals for the distribution, density and
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/va...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
University of Bologna
2013-05-01
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| Series: | Statistica |
| Online Access: | http://rivista-statistica.unibo.it/article/view/3535 |
| Summary: | 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. |
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| ISSN: | 0390-590X 1973-2201 |