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| Title: | 基於保序迴歸估計的資料遞增性檢定
Testing for an increasing trend based on isotonic regression |
| Authors: | 黃鈺茹
Huang, Yu-Ju |
| Contributors: | 黃子銘
黃鈺茹
Huang, Yu-Ju |
| Keywords: | 保序迴歸
遞增性檢定
濾波器
週期圖
Isotonic regression
PAVA
Filter
Periodogram
Examine the increasing trend |
| Date: | 2018 |
| Issue Date: | 2018-08-06 18:09:46 (UTC+8) |
| Abstract: | 本研究目的是在檢測時間序列資料是否隨時間遞增。本文中提出先估算資料的週期，再使用濾波器消除週期，再檢驗資料的遞增趨勢。在檢定遞增趨勢時，使用保序迴歸及逐段迴歸配適時間序列的趨勢，再以兩種趨勢的差距計算檢定統計量。本研究將所提出的方法應用於2015年北台灣的空氣品質資料，檢定結果發現大部分汙染物濃度並無遞增趨勢。
The purpose of this study is to test whether a time series has an increasing trend. This paper proposes to estimate the period of the time series first, then use a filter to eliminate the period, and then examine whether the filtered time series has an increasing trend. In examining the increasing trend, we use isotonic regression and piecewise regression to fit the trend of the time series, and then compute the difference between the fitted trends to obtain the test statistic. In this study, I apply the proposed method to the air quality data of North Taiwan in 2015. There are no increasing trends for most of the tested time series. |
| Reference: | [1] Barlow, R. E., Bartholomew, D. J., Bremner, J. M. and Brunk, H. D. (1972). Statistical Inference Under Order Restrictions: The Theory and Application of Isotonic Regression. New York : John Wiley & Sons.
[2] Best MJ, Chakravarti N. (1990). Active Set Algorithms for Isotonic Regression; A Unifying Framework. Mathematical Programming, 47(1-3):425–439.
[3] Brunk HB. (1955). Maximum Likelihood Estimates of Monotone Parameters. The Annals of Mathematical Statistics, 26(4):607–616.
[4] de Leeuw, J., Hornik, K. and Mair, P. (2009). Isotone Optimization in R: Pool-Adjacent-Violators Algorithm (PAVA) and Active Set Methods .Journal of Statistical Software, 32(5):1–24.
[5] Peter J. Brockwell and Richard A. Davis. (2002). Introduction to Time Series and Forecasting(2nd ed.). New York : Springer.
[6] Piet Groeneboom and Geurt Jongbloed. (2010). Generalized continuous isotonic regression. Statistics and Probability Letters,80 (3-4):248-253.
[7] Tibshirani, R., Hoefling, H. and Tibshirani, R. (2011). Nearly isotonic regression. Technometrics, 53(1):54–61.
[8] Tim Robertson, F. T. Wright and R. L. Dykstra. (1988). Order Restricted Statistical Inference. New York : John Wiley & Sons. |
| Description: | 碩士
國立政治大學
統計學系
105354028 |
| Source URI: | http://thesis.lib.nccu.edu.tw/record/#G0105354028 |
| Data Type: | thesis |
| DOI: | 10.6814/THE.NCCU.STAT.015.2018.B03 |
| Appears in Collections: | [統計學系] 學位論文
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| 402801.pdf | 2581Kb | Adobe PDF2 | 7 | View/Open |
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