LARGE AND MODERATE DEVIATIONS PRINCIPLES FOR KERNEL ESTIMATION OF A MULTIVARIATE DENSITY AND ITS PARTIAL DERIVATIVES | Zendy

Mokkadem Abdelkader | Zendy; Pelletier Mariane | Zendy; Worms Julien | Zendy

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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.

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