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    Title: 核多邊形圖的密度函數估計與適合度檢定
    Other Titles: Kernel Polygons for Density Function Estimation and Testing of Goodness of Fit
    Authors: 伍志祥
    Contributors: 淡江大學數學學系
    Keywords: Edge frequence polygon;Frequence polygon;Integrated mean squared error;Kernel polygon;Shift histogram
    Date: 2007
    Issue Date: 2009-03-16 13:13:48 (UTC+8)
    Abstract: 多邊形圖是一種計算快速簡單且經常被採用的估計量, Lin, C.T. Wu, J.S.&Yen, C.H (2006) 研究核多邊形圖,討論核多邊形圖成為一密度函數的充要條件,及最佳核多 邊形圖為何, 為了方便顯示大量資料的密度函數圖形可以快速的計算, Scoot, D.W.(1985b)提出shift histogram,若劃核多邊形圖時分割點的曲線估計量採用shift histogram ,會發現Lin, C.T. Wu, J.S.&Yen, C.H (2006)所建議的核函數,會造成偏差量 的收斂速度是平滑參數的一次方,而不是認知上的二次方.因此本計劃提出改善這個問 題的方法,及找出新族群所對應的最佳多邊形圖.另外由於用shift histogram 跟edge frequency 建造多邊形圖比用frequency histogram 建造的多邊形圖的MSE 要小很多, 本計劃將推廣Pearson』s 2 test,把frequency histogram 用shift histogram 跟edge frequency 這兩種估計量來取代, 並推導其漸近分佈,並比校Person』s 卡方檢定, scan test, Kolmogorov-Smirnov test 跟這新檢定的拒絕率.最後本計劃將把上面的結果及Lin, C.T. Wu, J.S.&Yen, C.H (2006)的研究推廣到高維度.讓這些結果有更廣的應用性.
    Appears in Collections:[Graduate Institute & Department of Mathematics] Research Paper

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