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

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莊坤翰(Kun-Han Zhuang) 查詢紙本館藏

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數學系

論文名稱

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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摘要(中)

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。

摘要(英)

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.

關鍵字(中)

★ 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

關鍵字(英)

★ backward selection
★ functional data analysis
★ multiresolution spline basis functions
★ multivariate analysis of variance
★ wearable devices

論文目次

1 概述（頁碼1）
2 資料與方法介紹（頁碼4）
2.1 資料簡介與前處理（頁碼4）
2.2 兩步驟函數型資料共變異數分析法（頁碼8）
2.3 步驟ㄧ:維度縮減（頁碼8）
2.4 步驟二:共變異數分析與變數選擇（頁碼11）
2.5 非齊性共變異矩陣分析法（頁碼14）
3 統計模擬（頁碼15）
3.1 模擬實驗1:0個有效解釋變數（頁碼15）
3.2 模擬實驗2:1個有效解釋變數（頁碼17）
3.3 模擬實驗3:2個有效解釋變數（頁碼19）
3.4 模擬實驗總結（頁碼21）
4 實際資料分析（頁碼23）
5 結論（頁碼25）
Reference（頁碼26）

參考文獻

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Tzeng, S. and Huang, H.-C. (2018). Resolution adaptive fixed rank kriging. Tech- nometrics, 60(2), 198-208.
Xu, S. Y., S, Nelson, S., Kerr, J., Godbole, S., Johnson, E., Patterson, R. E., Rock, C. L., Sears, D. D., Abramson, I., and Natarajan, L. (2019). Modeling temporal variation in physical activity using functional principal components analysis. Statistics in Biosciences, 11, 403-421.
Zhang, J. -T. (2012). An Approximate Hotelling T 2 -Test for Heteroscedastic One- Way MANOVA. Open Journal of Statistics, 2(01), 1-11.

指導教授

黃世豪(Shih-Hao Huang)

審核日期

2021-8-23

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