## The Annals of Statistics

### A Density-Quantile Function Approach to Optimal Spacing Selection

R. L. Eubank

#### Abstract

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.

#### Article information

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

Dates
First available in Project Euclid: 12 April 2007

https://projecteuclid.org/euclid.aos/1176345454

Digital Object Identifier
doi:10.1214/aos/1176345454

Mathematical Reviews number (MathSciNet)
MR615426

Zentralblatt MATH identifier
0477.62074

JSTOR

#### Citation

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. https://projecteuclid.org/euclid.aos/1176345454