線穿越及點穿越實驗中之廣義乘法測量誤差模型

Generalized Multiplicative Measurement Error in Line Transect and Point Transect Experiments

陳宛平(Wan-Ping Chen)

指導教授 ： 黃逸輝

淡江大學/理學院/數學學系碩士班/碩士(2009年)

https://doi.org/10.6846/TKU.2009.00679

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。

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

並列摘要

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.

並列關鍵字

additive measurement error ； multiplicative measurement error ； distance sampling ； line transect ； point transect ； moment method ； kernel estimation ； population density

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.