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    Please use this identifier to cite or link to this item: https://nccur.lib.nccu.edu.tw/handle/140.119/3851


    Title: 橢球形區域之估計
    Other Titles: Estimation of an Elliptically Shaped Domain
    Authors: 蔡紋琦
    Keywords: 形狀;橢圓球;不連續點;最大擬似估計;貝氏估計;強收斂;二維Cramer-vonMises型檢定
    Shape;Ellipse;Discontinuities;Maximum likelihood estimate;Bayes estimate;Strong consistency;Bivariate Cramer-von Mises type of test
    Date: 2001
    Issue Date: 2007-04-18 16:36:48 (UTC+8)
    Publisher: 臺北市：國立政治大學統計學系
    Abstract: 設法去找出一個未知區域的形狀、大小、或位置在很多科學領域中常常是一件基本且關鍵的工作。例如對環境研究者而言，他們可能需要畫定出被某污染物所污染的區域；對地質學者而言，則他們可能需要找出某一特定礦物的分布範圍。而其統計語言可寫成：藉由區域中隨機觀察到的位置來推測整個可能散佈的範圍。假設S是一個有界我們想要估計的區域，則是所有可能之區域所收集起來的集合，譬如 S 是一個橢圓球，則是所有 橢圓球形狀區域所形成的集合。則對任何 一般情況，我們可以證明出最大擬似估計 和貝氏估計會強收斂到真正的區域(在差集合測度的距離之下)。不過對於其極限分佈，目前則只能做到用二維的 Cramer-von Mises 型檢定來做檢查，此一方法有其缺失，即必須先給定一個可能的極限分佈，然後再做檢定，得到的並不是百分之百確定正確的分佈答案。
    Estimating the location, shape, and size of an unknown region of interest is usually an important task in many science disciplines. In environmental studies, the geographical spread of a pollutant is frequently crucial. In Geology, it is often required to find the covering area of a specific mineral substance. One general formulation of this kind of problem in Statistical language would be: estimating an unknown domain S of interest based on n points randomly selected from it. Let S be the bounded domain that we wish to estimate and be the collection of the domains with certain features that we believe S owns. For example, S is an ellipse and is the ellipse family. Under some weak conditions on , we can show that the maximum likelihood estimate and the Bayes estimate are strongly consistent with respect to the set-difference distance. As to the limiting distribution, the exact formulation is still not available. So far, we are able to use the bivariate Cramer-von Mises type of test to check for any possible limiting distribution of the estimates. However, it does not provide a 100% sure conclusions.
    Description: 核定金額：315300元
    Data Type: report
    Appears in Collections:[統計學系] 國科會研究計畫

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