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Large Deviations Limit Theorems for the Kernel Density Estimator
Author(s) -
Louani Djamal
Publication year - 1998
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/1467-9469.00101
Subject(s) - mathematics , pointwise , kernel density estimation , estimator , kernel (algebra) , variable kernel density estimation , large deviations theory , random variable , independent and identically distributed random variables , multivariate kernel density estimation , probability density function , limit (mathematics) , statistics , central limit theorem , kernel method , mathematical analysis , discrete mathematics , artificial intelligence , computer science , support vector machine
We establish pointwise and uniform large deviations limit theorems of Chernoff‐type for the non‐parametric kernel density estimator based on a sequence of independent and identically distributed random variables. The limits are well‐identified and depend upon the underlying kernel and density function. We derive then some implications of our results in the study of asymptotic efficiency of the goodness‐of‐fit test based on the maximal deviation of the kernel density estimator as well as the inaccuracy rate of this estimate