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Making a non‐parametric density estimator more attractive, and more accurate, by data perturbation
Author(s) -
Doosti Hassan,
Hall Peter
Publication year - 2016
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.12120
Subject(s) - estimator , sharpening , kernel density estimation , parametric statistics , perturbation (astronomy) , mathematics , kernel (algebra) , computer science , nonparametric statistics , statistical physics , mathematical optimization , econometrics , statistics , physics , artificial intelligence , quantum mechanics , combinatorics
Summary Motivated by both the shortcomings of high order density estimators, and the increasingly large data sets in many areas of modern science, we introduce new high order, non‐parametric density estimators that are guaranteed to be positive and do not have highly oscillatory tails. Our approach is based on data perturbation, e.g. by tilting or data sharpening. It leads to new estimators that are more accurate than conventional kernel techniques that use positive kernels, but which nevertheless enjoy the positivity property, and are far less ‘wiggly’ than high order kernel estimators. We investigate performance by theoretical analysis and in a numerical study.