臺灣博碩士論文加值系統

在生態統計上，我們藉由許多不同的方法去估計物種數，但是並不是所有的估計方法都可以精確估計出物種數。許多文獻上常使用Quenouille-Tukey 摺刀估計法去進行估計與修正其偏差， Burnham & Overton (1978) 建議使用此方法來估計母體數或物種數，接著提出使用假設檢定去決定適合的摺刀階數，檢定後摺刀估計量標準差為本文所主要關心的部分，因為所決定的階次k*是變動的，應該視為隨機變量，因此，Burnham & Overton(1978) 認為摺刀估計法的變異數估計是不可靠的，所以考慮使用變異數分解去做運算，為了驗證所提出的方法是否有效，進行了全面的模擬研究，將建議的估計量與現有的估計值進行比較，此外，所提過出方法通過一些實際資料分析來進行說明。

In the ecological literature, there are many estimators proposed to estimate the number of species in an assemblage, but, inevitably, not all of them can accurately estimate the true number of interest. Jackknife methods were very popular tools that are often used to correct the estimating bias of a biased estimator. Burnham & Overton (1978) suggested using the technique to estimate the population size (or equivalent to estimate the number of species). Additionally, they provided a criterion of sequential tests to determine a suitable jackknife order. However, the selected order is not a fixed number, instead it should be treated as a random variable. As a result, the variance estimation of the selected jackknife estimator is not reliable in Burnham & Overton (1978) who kept it as a constant. In the present work, we suggest applying the variance decomposition formula to derive a variance estimator of the selected jackknife estimator. For demonstrating the power of the proposed method, we conducted a comprehensive simulation study to compare the suggested estimator with the existed one. Moreover, the proposed method was practically illustrated by some real data analyses.

目錄
中文摘要 i
Abstract ii
表目次 iv
圖目次 vi
第一章 緒論 1
第二章 符號介紹與文獻探討 3
2.1 符號介紹 3
2.2 取樣模式 4
2.3 摺刀估計法的文獻探討 4
第三章 估計方法與階次決定規則 9
3.1 摺刀估計法 9
3.2 變異數 - δ-method 11
3.3 階次決定規則 12
3.4 變異數 - 變異數分解 12
第四章 模擬與實際資料分析 16
4.1 模擬分析 16
4.1.1 模擬分析說明 16
4.1.2 模擬分析結果 19
4.2 實際資料分析 23
第五章 結論 27
參考文獻 29
附錄 31

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