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截尾平均數

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(1)國 立 交 通 大 學 統 計 學 研 究 所 碩 士 論 文. 截尾平均數 Trimmed Mean. 研究生:林雅靜(Ya-Ching Lin) 指導教授:陳鄰安博士(Dr. Lin-An Chen). 中華民國九十四年六月.

(2) 截尾平均數. Trimmed Mean. 研 究 生:林雅靜. Student:Ya-Ching Lin. 指導教授:陳鄰安. Advisor:Dr. Lin-An Chen. 國立交通大學理學院 統計學研究所 碩士論文. A Thesis Submitted to Institute of Statistics College of Science National Chiao Tung University In Partial Fulfillment of the Requirements For the Degree of Master In Statistics June 2005 Hsinchu, Taiwan, Republic of Chhina 中華民國九十四年六月.

(3) 截尾平均數. 研 究 生:林雅靜. 指導教授:陳鄰安. 國立交通大學統計學研究所. 摘. 要. 我們介紹一種新的截尾平均數,稱為眾數截尾平均數。 衡量估計量穩健與否,破壞點是一個重要的準則,目前被提 出的穩健估計量中,破壞點皆小於或等於 0.5,我們將證明 眾數截尾平均數的破壞點可以趨近於 1。藉由模擬比較傳統 截尾平均數和眾數截尾平均數的均方差。更進一步介紹及探 討由眾數截尾平均數延伸建構出的一種新的 Winsorized 平均數。.

(4) Trimmed Mean Student:Ya-Ching Lin. Advisor:Dr. Lin-An Chen. Institute of Statistics National Chiao Tung University Hsinchu, Taiwan. Abstract We introduce a new type of trimmed mean, called the mode type trimmed mean. With the fact that the breakdown point is one important criterion for measuring the robust type estimators and the fact that the proposed robust estimators are all with breakdown points less than or equal to 0.5(see this point in Hampel et al. (1986)),we will show that this new trimmed mean may have breakdown point as large as close to 1. Simulation for comparing this trimmed mean and the traditional one will also be conducted through the mean square error (MSE). Moreover, an extension of this new type of trimmed mean to construct a new Winsorized mean will also be introduced and studied..

(5) 誌. 謝. 在口試通過的當下,所有的感動溢於言表。 這兩年能順利完成這篇論文,首先由衷地感謝我的指導 教授—陳鄰安老師,除了在課業上帶我循序漸進以外,在許 多面對事情的態度以及處理事情的方法上都讓我獲益良 多。還有感謝洪慧念老師、許文郁老師以及黃榮臣老師三位 口試委員撥冗指導。也要感謝交大統計所的師長,助理以及 同學們營造出一個絕佳的學習環境。也感謝同學們,揚波、 婉菁、碰仔…等,平時在論文上給我的建議和切磋。更要感 謝我的好朋友們,毓成、如美、秀仁…等,這一路上有你們 的加油打氣使我兩年來能勇敢的面對所有的困難。 最後要感謝我的父母—林來枝先生以及吳梅葉女士還 有家人們,謝謝他們在經濟上和精神上的支持跟信任,讓我 有個可以盡情發揮的空間。. 林雅靜 謹誌於交大統計所 九十四年六月.

(6) Contents 1. Introduction. 1. 2. Breakdown point for some robust location estimators. 3. 3. Mode type trimmed mean. 5. 4. Nonparametric estimation of trimmed mean. 8. 5. Nonparametric estimation of winsorized mean. 12. 6. Conclusion. 17. Reference. 17.

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