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系統識別號 U0002-1907200913054800
中文論文名稱 線穿越及點穿越實驗中之廣義乘法測量誤差模型
英文論文名稱 Generalized Multiplicative Measurement Error in Line Transect and Point Transect Experiments
校院名稱 淡江大學
系所名稱(中) 數學學系碩士班
系所名稱(英) Department of Mathematics
學年度 97
學期 2
出版年 98
研究生中文姓名 陳宛平
研究生英文姓名 Wan-Ping Chen
學號 696190460
學位類別 碩士
語文別 英文
口試日期 2009-06-24
論文頁數 27頁
口試委員 指導教授-黃逸輝
委員-黃文瀚
委員-溫啓仲
中文關鍵字 加法測量誤差  乘法測量誤差  距離抽樣  線穿越  點穿越  動差法  平滑技巧  母體密度 
英文關鍵字 additive measurement error  multiplicative measurement error  distance sampling  line transect  point transect  moment method  kernel estimation  population density 
學科別分類 學科別自然科學數學
中文摘要 在生態學中,調查對象的密度或總數是相當重要的參數,而距離抽樣則是方便且常採用的抽樣方法,本文討論的距離抽樣包括線穿越和點穿越兩種,並且是觀測距離無法精準量測而有測量誤差時的統計分析問題。我們考慮不同的測量誤差模型,先分別回顧以前的加法測量誤差模型和乘法誤差模型,進而考慮較新的廣義乘法誤差模型,最後探討新誤差模型下的估計問題。而主要的估計方法有兩種,分別是平滑技巧和動差法。本文利用廣泛的模擬試驗評估不同誤差模型下兩種估計方法的表現。
英文摘要 The population density is of great interest in ecology. We consider the measurement error in distance sampling which includes the line transect and point transect experiments. Different measurement error models were considered. The additive error model, the multiplicative error model and the generalized multiplicative error model are reviewed and discussed separately. Estimations by kernel method and moment method are reviewed or developed for different error models and their performances were assessed by extensive simulation studies.
論文目次 1. Introduction 1
2. Line Transect Sampling 2
2.1 Notation 2
2.2 Review of Estimation methods 3
2.3 Measurement Error 5
2.3.1 Additive Measurement Error 5
2.3.2 Multiplicative Measurement Error 6
2.3.3 Log-additive Measurement Error 7
3. Point Transect Sampling 10
3.1 Notation 11
3.2 Estimation Method 11
3.3 Measurement Error 13
3.3.1 Log-additive Measurement Error 14
4. Simulation of Experiment 17
5. Conclusion 19
Appendix 21
Reference 23
Table of Contents
Table 1 Line transect of parameter $p$ unknown
(N=500, $sigma_z^2=0.1$, $D=0.055$) 24
Table 2 Line transect of parameter $p$ unknown
(N=500, $sigma_z^2=0.05$, $D=0.055$) 24
Table 3 Line transect of parameter $p$ unknown
(N=1000, $sigma_z^2=0.1$, $D=0.055$) 25
Table 4 Line transect of parameter $p$ unknown
(N=1000, $sigma_z^2=0.05$, $D=0.055$) 25
Table 5 Point transect of parameter $p$ unknown
(N=500, $sigma_z^2=0.1$, $D=0.1768$) 26
Table 6 Point transect of parameter $p$ unknown
(N=500, $sigma_z^2=0.05$, $D=0.1768$) 26
Table 7 Point transect of parameter $p$ unknown
(N=1000, $sigma_z^2=0.1$, $D=0.3537$) 27
Table 8 Point transect of parameter $p$ unknown
(N=1000, $sigma_z^2=0.05$, $D=0.3537$) 27
參考文獻 Buckland, S. T. (1987). On the variable circular plot method of estimating animal density. Biometrics 43, 363-384.
Chen, S. X. (1998). Measurement error in line transect surveys. Biometrics 54,899-908.
Chen, S. X. , Cowling, A. (2001). Measurement errors in line transect surveys where delectability varies with distance and size. Biometrics 57, 732-742.
Mack, Y. P. , Quang,P.X. (1998). Kernel methods in line and point transect sampling. Biometrics 54, 606-619.
Marques, T. A. (2004). Predicting and correcting bias caused by measurement error in line transect sampling using multiplicative error models. Biometrics 60, 757-763.
Pollock, K. H. (1978). A family of density for line-transect sampling. Biometrics 34, 475-478.
Quang, P. X. (1993). Nonparametric estimators for variable circular plot surveys. Biometrics 49, 837-852.
Ramsey, F. L. and Scott, J. M. (1979). Estimating population densities from variable circular plot surveys. In Sampling Biological Population, R. M. Cormack, G. P. Patil, and D.S. Robson (eds), 155-181. Fairland, Maryland: International Publishing House.
Shu, Y. H. (2007). 線上穿越模式中有乘法測量誤差時之分析. 淡江大學數學學系碩士班碩士論文.
Williams, R. , Leaper, R. , Zerbini, A. N. and Hammond, P. S. . Methods for
investigating measurement error in cetacean line-transect surveys. F. Mar. Biol. Ass. U.K., 87, 313-320.
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