臺灣博碩士論文加值系統

有關母體總數估計研究至今已有一段很長的歷史，且已廣為應用，在此研究領域中，一般可分為封閉性母體與開放性母體兩種。在封閉母體下，通常假設動物的捕取歷史是完整的(completely data)，然而在實務上，卻可能因為被捕取動物缺失記號，或調查者記號登錄錯誤、記錄缺失，而造成捕取歷史的不完整。故本文針對在封閉母體下，假設動物捕取機率不同，研究當資料有紀錄失誤時，失誤機率值對既有的估計量所造成的偏差，以及如果捕取歷史資料是完全隨機失誤(missing completely at random )或是隨機失誤(missing at random)時，對母體總數的估計是否有影響，並提出修正的估計方法來彌補因失誤值所造成的偏差。

The analysis of the population size estimation has a long history and has been widely used in many applications. In this research field, it usually can be divided into the open population and the closed population. Under the closed population, we often assumed capture history of animals is the completely data. However, in the practical applications, animals maybe lose marks during sampling periods, records mistake of the marks or records lost. It causes the capture history of animals incomplete. Therefore, this paper studies the estimators of population size for the closed population. The bias of the estimators under complete capture-recapture data and capture history with missing data are compared. Two biases will be compared when capture history data are generated with missing completely at random and the probability that capture history data is missing depends on the capture-recapture data value. Finally, a bias corrected estimator is proposed.

CONTENTS
ABSTRACT ………………………………………………………………………….I
CONTENTS………………………………………………………………………...IV
LIST OF TABLES………………………………………………………………….. V
LIST OF FIGURES……………………………………………………………….. VI
1. INTRODUCTION…………………………………………………………………1
2. LITERATURE REVIEW…………………………………………………………3
2.1 Notation……………………………………………………………………….. 3
2.2 Literature review…………………………………………………………….....4
3. PROPOSED ESTIMATORS…………………………………………………….11
3.1 Sample coverage……………………………………………………………….11
3.2 The usual handle methods under capture history with missing data ………….12
3.3 The bias-corrected estimators………………………………………………….14
4. SIMULATION STUDY ………………………………………………………….19
4.1 Simulation procedure………………………………………………………….19
4.2 Simulation results ……………………………………………………………..21
4.3 Numerical Example……………………………………………………………27
5. CONCLUSION …………………………………………………………………..30
REFERENCE ……………………………………………………………………....32
APPENDIX A ……………………………………………………………………..35
APPENDIX B ……………………………………………………………………..38

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