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    题名: 測量誤差模式中的延伸校正分數函數
    其它题名: Extensively Corrected Scores in Measurement Error Models
    作者: 黃逸輝
    贡献者: 淡江大學數學學系
    关键词: 測量誤差模式;校正分數函數;條件分數函數;延伸校正分數函數;measurement errors;corrected score;conditional score;extensively corrected score
    日期: 2013-08
    上传时间: 2015-04-21 14:35:08 (UTC+8)
    摘要: 在測量誤差模型的分析方法中,傳統上只有校正分數函數及條件分數函數的結果具 有一致性,然而它們的應用受到許多限制;例如校正分數函數的存在要求被估計函數 必須是一個複數平面上的entire function,而條件分數函數則需要能找到缺失自變數 的充分統計量,這些假設限制了這兩個方法的應用範圍。本計畫預計發展一種新的估 計方法,我們並不打算直接估計原始的分數函數,因為該函數可能無法被不偏地估計 (Stefanski,1989),反而是估計加權後的分數函數,得到”加權的分數函數”的估計 量後我們再利用權重的近似值將結果”反加權”回來,最後所得的函數我們稱為延伸 校正分數函數。我們預期延伸校正分數函數除了有一致性外也會有不錯的效率,它也 可以應用於條件分數函數及校正分數函數皆不適宜的情況。
    There are two major consistent estimations in measurement error problems. The conditional score and the corrected score. The former method requires a sufficient statistic for the true covariate can be found, while the later method requires that the object score function can be estimated unbiasedly by surrogates and responses. Due to these assumptions, they are not applicable even for some simple models. For example, they are not applicable for the logistic regression with quadratic predictor. In this project, we will develop a novel method for estimating the object function. In stead of directly estimating the original score function which can be difficult or impossible, we will estimate a weighted version of it, and then reweigh it back for efficiency concern. Though the resultant function, the extensively corrected score, is not an unbiased estimator of the original score function, it has 0-mean property and converge to the original score function when measurement error approaches 0. It should be more flexible and applicable than the two traditional methods. We expect it to yield consistent estimates with good efficiencies.
    显示于类别:[數學學系暨研究所] 研究報告

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