The Annals of Statistics

A Density-Quantile Function Approach to Optimal Spacing Selection

R. L. Eubank

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In this paper design techniques for continuous parameter time series regression analysis are employed to develop a general approach to optimal spacing selection for the linear estimation of location and scale parameters by sample quantiles from uncensored or censored samples. The spacings derived from this approach are asymptotically optimal in the sense that they result in near optimal asymptotic relative efficiencies for large values of $k$, the number of spacing elements. A comparison with the optimum efficiencies for several distribution types indicates that the asymptotically optimum spacings perform well for $k \geq 7$. The regression framework is also utilized to develop sufficient conditions for optimal spacing unicity and to obtain asymptotically optimal spacings for quantile estimation.

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Ann. Statist., Volume 9, Number 3 (1981), 494-500.

First available in Project Euclid: 12 April 2007

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Primary: 62F99: None of the above, but in this section
Secondary: 62M99: None of the above, but in this section 62F10: Point estimation 62F12: Asymptotic properties of estimators

Order statistics estimation location parameter scale parameter censored samples quantile estimation reproducing kernel Hilbert space


Eubank, R. L. A Density-Quantile Function Approach to Optimal Spacing Selection. Ann. Statist. 9 (1981), no. 3, 494--500. doi:10.1214/aos/1176345454.

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