The Annals of Statistics

Uniform consistency of generalized kernel estimators of quantile density

C. Cheng

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Various smoothing methods for quantile density estimation are unified into a generalized kernel smoothing. Based on a stochastic upper bound of the derivatives sequence for a sequence of smoothed Brownian bridges, uniform in-probability consistency of generalized kernel quantile density estimators on any closed subinterval of the open unit interval is derived.

Article information

Ann. Statist., Volume 23, Number 6 (1995), 2285-2291.

First available in Project Euclid: 15 October 2002

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62G07: Density estimation 62G20: Asymptotic properties
Secondary: 62G05: Estimation 62G30: Order statistics; empirical distribution functions

Quantile density function approximation smoothing kernel


Cheng, C. Uniform consistency of generalized kernel estimators of quantile density. Ann. Statist. 23 (1995), no. 6, 2285--2291. doi:10.1214/aos/1034713657.

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