迴歸眾數區間
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(2) 迴歸眾數區間 Regression Mode Interval. 研 究 生：林貞佑. Student：Chen-Yiao Lin. 指導教授：陳鄰安. Advisor：Dr. Lin-An Chen. 國 立 交 通 大 學 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 2004 Hsinchu, Taiwan, Republic of China. 中華民國九十三年六月.
(3) 迴歸眾數區間. 學生:林貞佑. 指導教授:陳鄰安博士. 國立交通大學統計學研究所. 摘要. 在這篇文章中我們推廣了 Huang (2003)的眾數型區間到線性迴歸的問 題上。迴歸的眾數型態區間在某些分配下我們予以導出。在此一區間 的估計上，我們討論了有母數及無母數兩方面的方法及模擬分析。.
(4) Regression Mode Interval. Student: Chen-Yiao Lin. Advisor: Dr. Lin-An Chen. Institute of Statistics National Chiao Tung University. Abstract. In this paper, we extend the concept of the mode type quantile interval of Huang (2003) for the linear regression model. The population type mode interval for some distributions are derived and their estimation in parametric and nonparametric ways are introduced. Simulations for nonparametric estimation and trimmed means based on this quantile interval are done in comparison with those techniques based on the traditional symmetric type intervals..
(5) 致. 謝. 非常感謝陳鄰安老師傾力的教導與協助，並且非常有耐心、不 厭其煩的指導我完成這篇論文，在此致上最崇高的敬意與祝福。也要 感謝陳志榮老師、黃信誠老師以及許文郁老師，在口試時給我建議， 並指正我論文裡需要修改的地方。 在交大統研所的兩年，感謝所上老師精闢與隨和的授課，讓我 受益匪淺，我很幸運的能在這麼好的環境裡學習。 另外，也要感謝我的家人以及朋友們，在我感到沮喪及挫折時， 給我加油打氣，扶持我走過學習路上的低潮期，謝謝你們！. 林貞佑 2004.6..
(6) CONTENTS ABSTRACT (in Chinese) ABSTRACT (in English) ACKNOWLEDGEMENTS (in Chinese) CONTENTS LIST OF TABLES. i ii iii iv v. 1. Introduction……………………………………………….. 1 2. Population Type Regression Mode Interval………………. 3 3. Parametric Formulation of Regression Mode Interval…..... 6 4. Data Analysis..……………………………………………. 9 5. Nonparametric Study and Monte Carlo Simulation……... 12 6. Trimmed Means based on Regression Mode Interval…….16 Reference…………………………………………………….19.
(7) LIST OF TABLES Table 1. Powers for quantile intervals as control charts………. 9 Table 2. Estimated regression median and mode type intervals for the computer repairing data....................................10 Table 3. Estimated regression median and mode type intervals of 90% for the computer repairing data.......................11 Table 4. Estimated regression median and mode type intervals for the liquid data…………………………………….12 Table 5. MSE’s with Exponential error distributions................14 Table 6. MSE’s with Gamma error distributions Gamma(a,b)………………………………………….15 Table 7. MSE’s with Normal error distributions.......................16 Table 8. MSE’s for trimmed means and LSE under Gamma distribution ((a,b)=(4,1))……………………………..20 Table 9. MSE’s for trimmed means and LSE under Gamma distribution ((a,b)=(4,5))……………………………..21.
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