系統識別號 | U0002-1907200913054800 |
---|---|
DOI | 10.6846/TKU.2009.00679 |
論文名稱(中文) | 線穿越及點穿越實驗中之廣義乘法測量誤差模型 |
論文名稱(英文) | Generalized Multiplicative Measurement Error in Line Transect and Point Transect Experiments |
第三語言論文名稱 | |
校院名稱 | 淡江大學 |
系所名稱(中文) | 數學學系碩士班 |
系所名稱(英文) | Department of Mathematics |
外國學位學校名稱 | |
外國學位學院名稱 | |
外國學位研究所名稱 | |
學年度 | 97 |
學期 | 2 |
出版年 | 98 |
研究生(中文) | 陳宛平 |
研究生(英文) | Wan-Ping Chen |
學號 | 696190460 |
學位類別 | 碩士 |
語言別 | 英文 |
第二語言別 | |
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 |
關鍵字(中) |
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 |
關鍵字(英) |
additive measurement error multiplicative measurement error distance sampling line transect point transect moment method kernel estimation population density |
第三語言關鍵字 | |
學科別分類 | |
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. |
第三語言摘要 | |
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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