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題名 | Maximizing the Variance of Redescending M-Estimates when Scale is Unknown in A Contamination Model=混淆模式中當尺度為未知時再遞降M-估值最大變方之研究 |
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作者 | 蘇秀媛; |
期刊 | 國立臺灣大學農學院研究報告 |
出版日期 | 19930600 |
卷期 | 33:2 1993.06[民82.06] |
頁次 | 頁126-140 |
分類號 | 319.5 |
語文 | eng |
關鍵詞 | M-估值; 尺度; 混淆模式; 最大變方; 漸近變; 輔佐尺度估值; 分位差距; 對稱混淆; 動差空間法; M-estimate; Asymptotic variance; Auxiliary scale estimator; Interquantile range; Symmetric contamination; Method of moment space; |
中文摘要 | 以往在混淆對稱模式下,計算位置參數之M-估值之最大變方時,均假 設尺度參數為已知數。故實際上,當無法得知尺度參數時,此種做法是不正確的。 本文係利用樣本分布之分位差距做為輔佐尺度估值S(F),而進行再遞降φ函數 M-估值最大理方之計算。此最大變方之計算問題原為無限維問題,若將S(F)固定 為s,即在S(F)=s之條件下,此問題可由無限維減為至多為五維之問題,即僅須 求五個未知值。故對所有s而言,則成六維之問題。在某些特殊情況下,此問題 甚至可減至一維或二維,因此可大為簡化最大變方計算過程。 |
英文摘要 | In the study of evaluating maximum variance of M -estimate oflocation, the value of the scale parameter is usually assumed to beknown. The problem considered here is that of maximizingasymptotic variance of M -estimators of location for redescendingscore function φ with an auxiliary estimate of scale when scaleparameter is unknown. The auxiliary scale estimator is the a-interquantile range of the sample distribution S (F). Let s and sdenote the infirnum and the supremum of S (F) respectively. Forfixed s [s, s], the original infinite-dimensional problem ofmaximizing asymptotic variance over the contamination model can bereduced to at worst a 5-dimensional problem. Therefore, the wholevariance-maximizing problem over all s is at worst 6-dimensional.Moreover, under some special conditions on φ, for fixed s [s, s], weshow that the problem can further be reduced to one- or at worsttwo-dimensional. |
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