帶有錯誤分類與測量誤差數據的高維度變數選取與估計

Variable selection and estimation for misclassified responses and high-dimensional error-prone predictors

歐陽沁縈(Ou Yang Qin-Ying)

指導教授 ： 陳立榜

國立政治大學/商學院/統計學系/碩士(2022年)

https://doi.org/10.6814/NCCU202200889

摘要

二元分類一直是統計分析或監督式學習中值得被討論的內容。在建立二元結果與變數的模型選擇上,logistic 與 probit 的模型是較常被使用的。然而,在資料維度遽增以及不可忽視的測量誤差存在測量結果、變數當中,過去的傳統方法已不適用,這為我們在資料分析上帶來了重大的挑戰。為了解決上述的問題,我們提出有效的推論方法處理測量誤差並同時進行變數選取。具體來說,我們首先考慮 logistic 或 probit 的模型,將經過校正的應變數與自變數放入我們的估計函數中。接著,我們透過 boosting 方法去做變數選取並計算參數的估計值。在數值研究當中,我們所提出的方法能夠準確地保留重要變數且能精準地計算出估計參數。此外,經過誤差校正的結果在整體的分析表現上是顯著優於沒有校正的結果。

關鍵字

二元分類資料 ； boosting ； 誤差校正 ； 測量誤差 ； 回歸模型校正

並列摘要

Binary classification has been an attractive topic in statistical analysis or supervised learning. To model a binary response and predictors, logistic regression models or probit models are perhaps commonly used approaches. However, because of the rapid growth of the dimension of the data as well as the non ignorability of measurement error in responses and/or predictors, data analysis becomes challenging and conventional methods are invalid. To address those concerns, we propose a valid inferential method to deal with measurement error and handle variable selection simultaneously. Specifically, we primarily consider logistic regression models or probit models, and propose corrected estimating functions by incorporating error-eliminated responses and predictors. After that, we develop the boosting procedure with corrected estimating functions accommodated to do variable selection and estimation.Through numerical studies, we find that the proposed method accurately retains informative predictors as well as gives precise estimators, and its performance is generally better than that without measurement error correction.

並列關鍵字

binary data ； boosting ； error elimination ； measurement error ； regression calibration

參考文獻

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