Best linear invariant estimates of parameters of the largest extreme-value distribution from complete and from singly censored samples and its applications

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URI http://shark.lib.kagawa-u.ac.jp/kuir/metadata/2540
Title
Best linear invariant estimates of parameters of the largest extreme-value distribution from complete and from singly censored samples and its applications
Title Alternative
第一種極大値漸近分布母数の最良線形不変推定量とその応用
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Description

The problem of choosing the best estimators to estimate the parameters for the Type I asymptotic distribution of the largest extreme based on the first m order statistics of a sample of size n is considered, and the best linear invariant (BLI) estimators, which are best among linear estimators with mean squared error invariant under transformations, are presented and discussed. The weights for obtaining the BLI estimates and the mean squared errors of the estimators are given in Table I for 2≦m≦15, 2≦m≦n. Use of the BLI weights is illustrated by a detailed discussion of the case that a sample of size n can be assumed to be drawn from the Type I asymptotic distribution of the largest extreme. The BLI estimators, which have uniformly smaller mean squared errors than the Gauss-Markov best linear unbiased (BLU) estimators and which are simple linear functions of the BLU estimators, are found to yield estimates superior to others which have been proposed to deal with this problem.

第一種極大値漸近分布に従うn個の標本をランダムに抽出するとき, 最初のm個の順序統計量から分布母数を推定する方法について述べる. 推定量の選択基準として最小平均2乗誤差を考える. HARTER & MOORE および MANN の結果から最良線形不変推定量は最小平均2乗誤差をもつことがわかる. 最良線形不変推定量は最良線形不変推定量より一様に小さい平均2乗誤差をもち, 変換に対して平均2乗誤差は不変である. 最良線形不変推定値を求めるための重みと平均2乗誤差を2≦m≦15, 2≦m≦nについて表にした. その重みの使用方法について降雨データで説明した.

Author
著者 Kusanagi Yoshikazu
著者(ヨミ) クサナギ ヨシカズ
著者(別表記) 草薙 義一
著者 Fukuda Kiyoshi
著者(ヨミ) フクダ キヨシ
著者(別表記) 福田 清
Publication Title
香川大学農学部学術報告
Volume
31
Issue
1
Start Page
33
End Page
47
Publisher
香川大学農学部
Published Date
197909
ISSN
0368-5128
NCID
AN00038339
Resource Type
Departmental Bulletin Paper
Language
eng
Text Version
publisher
Set
香川大学
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