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系統識別號 U0026-2707201015352900
論文名稱(中文) 基因歧異性指標相等性試驗之統計評估
論文名稱(英文) Statistical Evaluation of Equivalence Test Based on the Genetic Diversity Index
校院名稱 成功大學
系所名稱(中) 統計學系碩博士班
系所名稱(英) Department of Statistics
學年度 98
學期 2
出版年 99
研究生(中文) 謝裕弘
研究生(英文) Yu-Hung hsieh
學號 r2697104
學位類別 碩士
語文別 英文
論文頁數 121頁
口試委員 口試委員-陳俞成
口試委員-潘宏裕
指導教授-馬瀰嘉
中文關鍵字 生物多樣性  相等性  核苷酸多樣性指標  Horvitz-Thompson  拔靴法 
英文關鍵字 biodiversity  equivalence  nucleotide index  Horvitz-Thompson  bootstrap-based approach 
學科別分類
中文摘要 聯合國宣布2010年為「國際生物多樣性年」,以彰顯地球上生命的千姿百態,生物學家時常將生物多樣性定義為「基因、物種及一個地區的生態系統之整體」,由此可知生物多樣性的重要。本研究專注於基因相等性來比較兩基因多樣性指標,特別是核苷酸多樣性指標。傳統多樣性估計忽略了沒有找到的基因類型,當這個基因是一種不可忽略的基因序列時會造成低估基因多樣性的結果。
因此,我們合併Horvitz-Thompson方法及採樣覆蓋範圍的觀念來獲取較佳的基因多樣性估計式,接著利用估計式及two one-sided檢定方法來檢定相等性。利用模擬研究來計算型I誤差發生機率及檢定力。此外在小樣本下,也利用拔靴法和two one-sided方法的結果來比較他們之間型I誤差發生機率及檢定力的差異。
英文摘要 The United Nations marked 2010 as the International Year of Biodiversity - the variety of life on Earth 2010. Biologists often define biodiversity as the "totality of genes, species, and ecosystems of a region". It is clear that the importance of biodiversity. This study is concerned with the equivalence for multi-categorical data and focuses on gene comparison by some genetic diversity index, especially in nucleotide diversity index. The traditional estimator of diversity ignores the missing gene types result in to underestimate the gene diversity, when there is a non-negligible number of unseen genetic sequence. Therefore we combine the concept of Horvitz-Thompson and sample coverage to obtain the better genetic diversity estimator. Then we use the estimator and two one-sided test method to test the equivalence. A simulation study was conducted to empirically investigate the size and power of the proposed methods. Besides, a bootstrap-based approach is also proposed in small sample size and compared with the two one-sided test by the size and power.
論文目次 Chapter 1 Introduction.................................1
Chapter 2 Literature Review............................4
2.1 Three Measurements of Gene Diversity................4
(Ⅰ) Definition .......................................4
(Ⅱ) Maximum Likelihood Estimator...................6
2.2 Bias Corrected Estimator............................7
(Ⅰ) Sample Coverage................................8
(Ⅱ) Horvitz-Thompson Estimator.....................10
2.3 The Statistical Methods for the Equivalence.........12
Chapter 3 Proposed Methods.............................16
3.1 The Estimators of Equivalence Test (S is known).16
3.2 The Estimators of Equivalence Test (S is unknown).19
Chapter 4 Simulation Study.............................23
4.1 Simulation Process..............................23
4.2 Bootstrap Procedure.............................26
4.3 Simulation results..............................26
4.3.1 Based on two one-sided method..............27
4.3.2 Based on bootstrap procedure...............29
4.3.3 Compare two one-sided method and bootstrap method....31
4.4 Real Example........................................32
Chapter 5 Discussion...................................34
Reference...............................................36

Appendix A..............................................39
Appendix B..............................................44
Appendix C..............................................49
Appendix D..............................................51
Appendix E..............................................57
Appendix F..............................................63
Appendix G..............................................87
Appendix H..............................................112
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