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Contents of PMS, Vol. 40, Fasc. 1,
pages 83 - 95
DOI: 10.37190/0208-4147.40.1.5
Published online 20.3.2020
 

MODERATE DEVIATION AND LARGE DEVIATION FOR WEGMAN--DAVIES RECURSIVE DENSITY ESTIMATORS

Yu Miao
Qinghui Gao
Jianyong Mu
Conghui Deng

Abstract: Let \(\{X_k, k\ge 1\}\) be a sequence of independent identically distributed random variables with common probability density function \(f\), and let \(\hat f_n\) denote a Wegman–Davies recursive density estimator \[ \hat f_n(x)=\frac{1}{nh_n^{1/2}}\sum_{j=1}^n\frac{1}{h_j^{1/2}} K\left(\frac{x-X_j}{h_j}\right) \] where \(K\) is a kernel function and \(h_n\) is a band sequence. In the present paper, the moderate deviation principle and the large deviation principle for the estimator \(\hat f_n\) are established.

2010 AMS Mathematics Subject Classification: Primary 62G07; Secondary 60F10.

Keywords and phrases: moderate deviation principle, large deviation principle, recursive kernel estimator

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