政大機構典藏-National Chengchi University Institutional Repository(NCCUR):Item 140.119/30945

政大機構典藏-National Chengchi University Institutional Repository(NCCUR):Item 140.119/30945

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政大機構典藏 > 商學院 > 統計學系 > 學位論文 > Item 140.119/30945

請使用永久網址來引用或連結此文件: https://nccur.lib.nccu.edu.tw/handle/140.119/30945

題名:	兩階段實驗設計在簡單迴歸轉換點估計上的應用 Two-stage design for estimation of the change point in a two-phase simple linear regression
作者:	賴進利 Lai, Jin-Li
貢獻者:	蔡紋琦 Tsai, Wen-Chi 賴進利 Lai, Jin-Li
關鍵詞:	轉換點 change point
日期:	2004
上傳時間:	2009-09-14
摘要:	轉換點(change point)問題出現在許多的統計領域，包括了有母數、無母數、迴歸、時間序列、序貫、貝式等模型，本研究主要是針對簡單迴歸模型的估計單一轉換點之問題作探討，若我們均勻分布解釋變數並採用最小平方法來估計轉換點，模擬結果告訴我們估計值會有雙峰的現象，此現象造成了變異數的增大。我們嘗試利用二階段設計來改善之前的估計，藉由第一階段所得到轉換點的可能範圍來估計第二階段的實驗，模擬結果顯示此兩階段估計的確降低了估計值的差異。 The change point problem can be involved in many models such as parametric, nonparametric, regression, time series, sequential, Bayesian, and so on. This thesis focuses on estimating the location of the change point in a simple regression model. We first show that the computational simulation demonstrates a bimodal phenomenon which could increase the variation of the estimator badly when the independent variables are allocated uniformly over the explanatory interval and the least square method is used to determine the estimator of the change point. In the second part,we implement a two-stage design that tries to shrink the possible location of the change point via first stage and then design the second stage accordingly. Simulation result gives a positive response in reducing the variation caused by the bimodal phenomenon.
參考文獻:	Chen, Jie , and Gupta, A. K. (1997), ""Testing and locating variance changepoints with application to stock prices``, Journal of the American Statistical Association, 92 , 739-747 Chen, Jie , and Gupta, A. K. (1999), ""Change point analysis of a Gaussian model``, Statistical Papers, 40 , 323-333 Chen, Jie , and Gupta, A. K. (2000), ""Parametric statistical change point analysis``, Birkh□user Verlag (Basel; Cambridge, MA) Choy, J. H. Chin , and Broemeling, L. D. (1980), ""Some Bayesian inferences for a changing linear model``, Technometrics, 22 , 71-78 Cs□rg□, M. , and Horv□th, Lajos (1997), ""Limit theorems in change-point analysis``, John Wiley & Sons (New York; Chichester) Darkhovskii, B. S. (1984), ""On two estimation problems for times of change of the probabilistic characteristics of a random sequence``, Theory of Probability and its Applications, 29 , 478-487 Hackl, P. and Westlund, A. H. (1989), "Statistical Analysis of “Structural Change”:An Annotated Bibliography``, empec, 14 , 167-192 Hawkins, Douglas M. (1977), ""Testing a sequence of observations for a shift in location``, Journal of the American Statistical Association, 72 , 180-186 Huskov□, Marie (1996), ""Estimation of a change in linear models``, Statistics & Probability Letters, 26 , 13-24 Krishnaiah, P. R. , and Miao, B. Q. (1988), ""Review about estimation of change points``, Handbook of Statistics Volume 7: Quality Control and Reliability, 375-402 Lee, Chung-Bow (1995), ""Estimating the number of change points in a sequence of independent normal random variables``, Statistics & Probability Letters, 25 , 241-248 Montgomery, D. C. (2001), ""Design and analysis of experiments``, John Wiley & Sons (New York; Chichester) Sitter, R. R. , and Forbes, B. E. (1997), ""Optimal two-stage designs for binary response experiments``, Statistica Sinica, 7 , 941-956 Sitter, R. R. , and Wu, C. F. J. (1999), ""Two-stage design of quantal response studies``, Biometrics, 55 , 396-402 Weerahandi, S. (1987), ""Testing regression equality with unequal variances``, Econometrica, 55 , 1211-1215 Westlund, A and Zackrisson, U (1986), ""On the prediction of structurally varing system``, Techn. Forecasting and Social Change, 30:63-72 Yakir, B. (1998), ""On the average run length to false alarm in surveillance problems which possess an invariance structure``, The Annals of Statistics, 26 (3) , 1198-1214 Yakir, B. , Krieger, A. M. , and Pollak, Moshe (1999), ""Detecting a change in regression: first-order optimality``, The Annals of Statistics, 27 (6) , 1896-1913 Yao, Y. C. (1988), ""Estimating the number of change-points via Schwarz` criterion``, Statistics & Probability Letters, 6 , 181-189
描述:	碩士國立政治大學統計研究所 92354013 93
資料來源:	http://thesis.lib.nccu.edu.tw/record/#G0923540131
資料類型:	thesis
顯示於類別:	[統計學系] 學位論文

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