Abstract
Linear functions of order statistics (“L‐estimates”) of the form Tn =under jackknifing are investigated. This paper proves that with suitable conditions on the function J, the jackknifed version Tn of the L‐estimate Tn has the same limit distribution as Tn. It is also shown that the jackknife estimate of the asymptotic variance of n1/2 is consistent. Furthermore, the Berry‐Esséen rate associated with asymptotic normality, and a law of the iterated logarithm of a class of jackknife L‐estimates, are characterized.
| Original language | English |
|---|---|
| Pages (from-to) | 49-58 |
| Number of pages | 10 |
| Journal | Canadian Journal of Statistics |
| Volume | 10 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 1982 |
| Externally published | Yes |
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Keywords
- asymptotic normality
- Berry‐Esséen rate
- Jackknife
- law of the iterated logarithm
- L‐estimate
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty
Cite this
Jackknifing L‐estimates. / Cheng, Kuang‐Fu ‐F.
In: Canadian Journal of Statistics, Vol. 10, No. 1, 1982, p. 49-58.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Jackknifing L‐estimates
AU - Cheng, Kuang‐Fu ‐F
PY - 1982
Y1 - 1982
N2 - Linear functions of order statistics (“L‐estimates”) of the form Tn =under jackknifing are investigated. This paper proves that with suitable conditions on the function J, the jackknifed version Tn of the L‐estimate Tn has the same limit distribution as Tn. It is also shown that the jackknife estimate of the asymptotic variance of n1/2 is consistent. Furthermore, the Berry‐Esséen rate associated with asymptotic normality, and a law of the iterated logarithm of a class of jackknife L‐estimates, are characterized.
AB - Linear functions of order statistics (“L‐estimates”) of the form Tn =under jackknifing are investigated. This paper proves that with suitable conditions on the function J, the jackknifed version Tn of the L‐estimate Tn has the same limit distribution as Tn. It is also shown that the jackknife estimate of the asymptotic variance of n1/2 is consistent. Furthermore, the Berry‐Esséen rate associated with asymptotic normality, and a law of the iterated logarithm of a class of jackknife L‐estimates, are characterized.
KW - asymptotic normality
KW - Berry‐Esséen rate
KW - Jackknife
KW - law of the iterated logarithm
KW - L‐estimate
UR - http://www.scopus.com/inward/record.url?scp=84988119580&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84988119580&partnerID=8YFLogxK
U2 - 10.2307/3315075
DO - 10.2307/3315075
M3 - Article
VL - 10
SP - 49
EP - 58
JO - Canadian Journal of Statistics
JF - Canadian Journal of Statistics
SN - 0319-5724
IS - 1
ER -