Moderate Deviations and Large Deviations for Kernel Density Estimators |
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Authors: | Fuqing Gao |
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Institution: | (1) School of Mathematics and Statistics, Wuhan University, Wuhan, 430072, People's Republic of China |
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Abstract: | Let f
n
be the non-parametric kernel density estimator based on a kernel function K and a sequence of independent and identically distributed random variables taking values in
d
. It is proved that if the kernel function is an integrable function with bounded variation, and the common density function f of the random variables is continuous and f(x) 0 as |x| , then the moderate deviation principle and large deviation principle for
hold. |
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Keywords: | kernel density estimator moderate deviations large deviations |
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