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NONPARAMETRIC QUANTILE ESTIMATION FROM RECORD‐BREAKING DATA
Author(s) -
Gulati Sneh,
Padgett W.J.
Publication year - 1994
Publication title -
australian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 0004-9581
DOI - 10.1111/j.1467-842x.1994.tb00863.x
Subject(s) - quantile , estimator , nonparametric statistics , smoothing , mathematics , statistics , sample (material) , sample size determination , econometrics , physics , thermodynamics
Summary Sometimes, in industrial quality control experiments and destructive stress testing, only values smaller than all previous ones are observed. Here we consider nonparametric quantile estimation, both the ‘sample quantile function’ and kernel‐type estimators, from such record‐breaking data. For a single record‐breaking sample, consistent estimation is not possible except in the extreme tails of the distribution. Hence replication is required, and for m. such independent record‐breaking samples the quantile estimators are shown to be strongly consistent and asymptotically normal as m‐→∞. Also, for small m , the mean‐squared errors, biases and smoothing parameters (for the smoothed estimators) are investigated through computer simulations.