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LARGE AND MODERATE DEVIATIONS PRINCIPLES FOR KERNEL ESTIMATION OF A MULTIVARIATE DENSITY AND ITS PARTIAL DERIVATIVES
Author(s) -
Mokkadem Abdelkader,
Pelletier Mariane,
Worms Julien
Publication year - 2005
Publication title -
australian and new zealand journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 1369-1473
DOI - 10.1111/j.1467-842x.2005.00411.x
Subject(s) - mathematics , estimator , kernel density estimation , kernel (algebra) , multivariate kernel density estimation , multivariate statistics , large deviations theory , statistics , quadratic equation , density estimation , variable kernel density estimation , kernel method , combinatorics , artificial intelligence , geometry , computer science , support vector machine
Summary This paper studies the large deviations behaviour of the kernel estimator of a probability density f , by considering the case when the kernel takes negative values. It establishes large and moderate deviations principles for the kernel estimators of the partial derivatives of f . The estimators of the derivatives exhibit a quadratic behaviour for both the large and the moderate deviations scales, whereas for the density estimator there is a classical gap between the large deviations and the moderate deviations asymptotics.