用於函數型資料之兩步驟共變異數分析在穿戴 裝置資料之應用;A two-step functional MANOVA with application to wearable device data

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題名:	用於函數型資料之兩步驟共變異數分析在穿戴裝置資料之應用;A two-step functional MANOVA with application to wearable device data
作者:	莊坤翰;Zhuang, Kun-Han
貢獻者:	數學系
關鍵詞:	向後選取法;函數型資料分析;多解析度樣條基底函數;多變量變異數分析;穿戴式裝置;backward selection;functional data analysis;multiresolution spline basis functions;multivariate analysis of variance;wearable devices
日期:	2021-08-23
上傳時間:	2021-12-07 13:10:43 (UTC+8)
出版者:	國立中央大學
摘要:	穿戴式裝置是穿戴在人體上記錄數據的設備，根據每分鐘運動強度提供客觀的運動測量值。近年來關於穿戴式裝置資料已經有很多的研究，此種資料常被視為函數型資料。在本論文中我們結合幾種已知的研究方法應用在這樣的函數型資料上，提出一個兩步驟分析方法。將資料整理成對齊的資料之後，首先我們以多解析度樣條基底函數(multiresolution spline basis functions)製作一個投影矩陣用以降低這筆資料的維度。這個投影矩陣被證明能在降低具空間相關性資料的維度時大致維持原始高維度資料的特徵。接著我們結合向後選取法 (backward selection)與多變量變異數分析(MANOVA)挑選出影響運動強度的主要因素。我們的三種模擬實驗顯示此方法的有效性和檢定力都不錯。本研究的實證分析資料為美國國家健康和營養檢查調查(National Health and Nutrition Examination Survey, NHANES)的穿戴式裝置數據。分析結果顯示性別為影響運動強度的重要變數。;Wearable devices, such as accelerometers, are person-worn sensors that are worn on human bodies to record data, and they provide objective mea- surements based on the intensity of exercise per minutes. In recent years, there has been a lot of studies on wearable devices, where this type of data are usually treated as functional data. We combine several well-known sta- tistical methods to analyse wearable device data. Our proposal has two steps after aligning the data. First, we project the data on the space spanned by multiresolution spline basis functions to reduce the dimensions of the data. This projection has been shown to roughly keep the characteristics of the original high-dimensional data with spatial structures. Next, we select the main factors affecting the activity intensity by applying backward selection and multivariate analysis of variance (MANOVA). Our three simulation ex- periments show that the validity and the efficiency of our method are well. We apply our approach on the wearable device data from National Health and Nutrition Examination Survey (NHANES). Our alalysis shows that the most important variables that affect activity counts is gender. Keywords: backward selection, functional data analysis, multiresolution spline basis functions, multivariate analysis of variance, wearable devices.
顯示於類別:	[數學研究所] 博碩士論文

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