Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
The empirical Edgeworth expansion for a Studentized trimmed mean. / Gribkova, N.V.; Helmers, R.
в: Mathematical Methods of Statistics, Том 15, № 1, 2006, стр. 61--87.Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
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TY - JOUR
T1 - The empirical Edgeworth expansion for a Studentized trimmed mean
AU - Gribkova, N.V.
AU - Helmers, R.
PY - 2006
Y1 - 2006
N2 - We establish the validity of the empirical Edgeworth expansion (EE) for a studentized trimmed mean, under the sole condition that the underlying distribution function of the observations satisfies a local smoothness condition near the two quantiles where the trimming occurs. A simple explicit formula for the N^{-1/2} term (correcting for skewness and bias; N being the sample size) of the EE is given. In particular our result supplements previous work by P. Hall and A.R. Padmanabhan, On the bootstrap and the trimmed mean}, J. of Multivariate Analysis, v. 41 (1992), pp. 132-153. and H. Putter and W.R. van Zwet, Empirical Edgeworth expansions for symmetric statistics, Ann. Statist., v. 26 (1998), pp. 1540-1569. The proof is based on a U-statistic type approximation and also uses a version of Bahadur's representation for sample quantiles.
AB - We establish the validity of the empirical Edgeworth expansion (EE) for a studentized trimmed mean, under the sole condition that the underlying distribution function of the observations satisfies a local smoothness condition near the two quantiles where the trimming occurs. A simple explicit formula for the N^{-1/2} term (correcting for skewness and bias; N being the sample size) of the EE is given. In particular our result supplements previous work by P. Hall and A.R. Padmanabhan, On the bootstrap and the trimmed mean}, J. of Multivariate Analysis, v. 41 (1992), pp. 132-153. and H. Putter and W.R. van Zwet, Empirical Edgeworth expansions for symmetric statistics, Ann. Statist., v. 26 (1998), pp. 1540-1569. The proof is based on a U-statistic type approximation and also uses a version of Bahadur's representation for sample quantiles.
KW - Empirical Edgeworth expansion
KW - Studentized trimmed mean
M3 - Article
VL - 15
SP - 61
EP - 87
JO - Mathematical Methods of Statistics
JF - Mathematical Methods of Statistics
SN - 1066-5307
IS - 1
ER -
ID: 5202035