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Preadjusted non‐parametric estimation of a conditional distribution function
Author(s) -
Veraverbeke Noël,
Gijbels Irène,
Omelka Marek
Publication year - 2014
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/rssb.12041
Subject(s) - estimator , quantile , conditional probability distribution , parametric statistics , mathematics , statistics , estimation , parametric model , econometrics , engineering , systems engineering
Summary The paper deals with non‐parametric estimation of a conditional distribution function. We suggest a method of preadjusting the original observations non‐parametrically through location and scale, to reduce the bias of the estimator. We derive the asymptotic properties of the estimator proposed. A simulation study investigating the finite sample performances of the estimators discussed is provided and reveals the gain that can be achieved. It is also shown how the idea of the preadjusting opens the path to improved estimators in other settings such as conditional quantile and density estimation, and conditional survival function estimation in the case of censored data.