廖振鐸Cheng, Chi-Lun;Liao, Chen-Tuo臺灣大學:農藝學研究所蔡嘉仁Tsai, Jia-RenJia-RenTsai2010-05-052018-07-112010-05-052018-07-112009U0001-0606200908364600http://ntur.lib.ntu.edu.tw//handle/246246/180099本篇論文主要探討的主題是線性誤差模型在測量誤差的變異是同質性或者異質性時之信賴區間估計。首先，當測量誤差的變異是同質性時，我們對斜率項參數建構信賴區間，除了回顧已發表的方法外，也提出一個新的方法，建議的區間方法分別和已存在的方法做模擬比較，比較的標準建構在覆蓋機率和平均長度上；另外，當測量誤差的變異是異質性時，我們不僅對斜率項參數建構信賴區間提出新的方法，也對截距項參數和斜率項參數建構聯合信賴區間。除了以實際例子說明建議的區間估計方法外，藉由蒙地卡羅模擬分析，建議的區間方法在覆蓋機率上也得到不錯的結果。The dissertation discusses interval estimation in linear regression model with homoscedastic and heteroscedastic measurement errors in both axes. First of all, we introduce some interval methods and propose a new approach to find confidence interval for the slope in homoscedastic measurement error models. The performance of the interval estimation is compared in terms of both coverage probability and its diameter via simulation studies. Second, we suggest two approaches to estimate confidence intervals for the slope and joint confidence regions for both intercept and slope in heteroscedastic measurement error models. Application of these methods are illustrated with real data sets. The performances of the confidence interval estimation are also studied numerically via Monte Carlo simulation in terms of coverage probability.中文摘要 iiibstract ivhapter 1 Introduction 1hapter 2 Linear homoscedastic measurement error models 7.1 A review of interval estimation 7.1.1 Interval estimation for the slope parameter 7emark 8.1.2 The confidence interval for error variance is known 9.2 Generalized confidence interval 11.3 Results of simulation and an example 14.3.1 Simulation studies 14.3.2 An example 16.4 Conclusions 16able 1 18able 2 20hapter 3 Linear heteroscedastic measurement error models 22.1 Confidence interval for the slope 22.1.1 Asymptotic confidence interval 23.1.2 Modified Creasy-Williams'' confidence interval 26emark 28.2 Joint confidence regions for intercept and slope 29.2.1 Asymptotic confidence region 29.2.2 Brown''s confidence region 30.3 Experimental part 31ata set 1 31igure 1 32ata set 2 33ata set 3 33ata set 4 34ata set 5 35ata set 6 35.4 Simulation studies 36.5 Concluding remarks 38ppendix A 40able 3 41able 4 42able 5 43able 6 48hapter 4 Conclusions and future research 50ibliography 52application/pdf548614 bytesapplication/pdfen-US信賴區間覆蓋機率期望長度異質性測量誤差同質性測量誤差確認性測量誤差模型Confidence intervalConverge probabilityExcepted lengthHeteroscedastic measurement errorsHomoscedastic measurement errorsIdentifiabilityMeasurement error modelsthesishttp://ntur.lib.ntu.edu.tw/bitstream/246246/180099/1/ntu-98-D92621202-1.pdf