Optimal spacing of the selected sample quantiles for the joint estimation of the location and scale parameters of a symmetric distribution |
| |
Authors: | Junjiro Ogawa |
| |
Institution: | Professor Emeritus of Statistics, The University of Calgary, Canada |
| |
Abstract: | We are considering the ABLUE’s – asymptotic best linear unbiased estimators – of the location parameter μ and the scale parameter σ of the population jointly based on a set of selected k sample quantiles, when the population distribution has the density of the formwhere the standardized function f(u) being of a known functional form.A set of selected sample quantiles with a designated spacingor in terms of u=(x−μ)/σwhereλi=∫−∞uif(t) dt, i=1,2,…,k are given bywhereAsymptotic distribution of the k sample quantiles when n is very large is given byh(x(n1),x(n2),…,x(nk);μ,σ)=(2πσ2)−k/2λ1(λ2−λ1)(λk−λk−1)(1−λk)]−1/2nk/2 exp(−nS/2σ2), whereThe relative efficiency of the joint estimation is given bywhereand κ being independent of the spacing
. The optimal spacing is the spacing which maximizes the relative efficiency η(μ,σ).We will prove the following rather remarkable theorem. Theorem. The optimal spacing for the joint estimation is symmetric, i.e.orif the standardized density f(u) of the population is differentiable infinitely many times and symmetricf(−u)=f(u), f′(−u)=−f′(u). |
| |
Keywords: | |
本文献已被 ScienceDirect 等数据库收录! |
|