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。

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.

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

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