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研究生:陳大昌
研究生(外文):Ta-Chang Chen
論文名稱:隨機過程在線性迴歸ME模型下的估計問題
論文名稱(外文):Estimates in linear regression ME modelsfor processes with uncorrelated increments
指導教授:吳鐵肩吳鐵肩引用關係
指導教授(外文):Tiee-Jian Wu
學位類別:碩士
校院名稱:國立成功大學
系所名稱:統計學系碩博士班
學門:數學及統計學門
學類:統計學類
論文種類:學術論文
論文出版年:2002
畢業學年度:90
語文別:英文
論文頁數:26
中文關鍵詞:Gauss-Markov 定理收斂隨機過程ME模型連續性線性迴歸
外文關鍵詞:Gauss-Markov theoremmeasurement error modelconsistencystochastic processes with uncorrelated incrementContinuous-time linear regression
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  • 被引用被引用:0
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  • 下載下載:87
  • 收藏至我的研究室書目清單書目收藏:2
近年來,在許多工業、生物科學及醫學上的資料是以精密儀器收集。因此我們所得到的資料是一段與時間有關的連續型曲線,在這一篇論文中,我們將提出一個方法估計隨機過程在線性迴歸ME模型下的參數。我們也建立在 Berkson model 下的 Gauss-Markov 定理。此外,也提出一些關於參數的收斂性質。
In recent years, a lot of industrial, biological, and medical processes are continuously monitored by instruments under the control of microprocessors. Thus, our data is a set of curves de ned on certain time interval. This paper presents a method of estimating parameters in the ME (measurement error ) model for a stochastic process with uncorrelated increments.Based on the sample path(s) of such process(es) the estimates of regression parameters are obtained. We establish a Gauss-Markov theorem for the proposed estimator in the multiple linear regression Berkson model. Furthermore, the consistency in q.m.(quadratic mean) of the proposed estimator is established.
Chapter 1 Introduction 1
Chapter 2 Literature Review 2
2.1 Classical discrete-time measurement error model 2
2.2 Modi ed least squares 4
2.3 Maximum likelihood estimation for the structural relationship with
correlated error 7
2.4 Berkson Model 9
2.5 Linear regression models (without measurement error) for processes
with uncorrelated increments 10
Chapter 3 Linear Regression Model with Measurement Error for Processes
with Uncorrelated Increments 12
3.1 Estimation of the parameters 13
3.2 Small and large sample properties 18
Chapter 4 Multiple Linear Regression Berkson Model 21
Reference 26
C.L. Cheng and John W. Van Ness, Statistical regression with measurement error, (Arnold,London, 1999).

C.L. Cheng and C.L. Tsai, Estimating linear measurement error models via M-estimators.In Symposia Gaussiana: Proceeding s of Second Gauss Symposium, Conference B: Statistical Sciences (eds V. Mammmitzsch and H. Schneeweiss) (1995) 247-259.

G.R. Dolby, The ultrastructural relation: a synthesis of the functional and structural relations.Biometrika, 63 (1976), 39-50.

J. Berkson Are there two regressions?, J. Amer. Statist. Assoc., 45 (1950) 164-180.

J.L. Doob, Stochastic processes, (Wiley, New York, 1953).

J.O. Ramsay, When the data are functions, Psychometrika 47 (1982) 379-396.

R.A. Olshen, E.N. Biden, M.P. Wyatt and D.H. Sutherland, Gait analysis and the bootstrap,Ann. Statist. 17 (1989) 1419-1440.

T.J. Wu and M.T. Wasan, Time integrated leasts squares estimators of regression parameters of independent stochastic processes, Stochastic Processes Appl. 35 (1990) 141-148.

T.J. Wu and M.T. Wasan, Weighted least squares estimates in linear regression models for processes with uncorrelated increments, stochastic processes and their applications 64(1996) 273-286.
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