臺灣博碩士論文加值系統

資料庫BDHS (Bangladesh Demographic and Health Survey) 提供孟加拉重要的健康資訊，包含婦女的生育過程。本論文探討婦女生育第二與第三胎時間之聯合分佈。由於資料必須挑選至少生育過兩胎的婦女，造成資料產生選擇性的偏誤，我們將之歸類於右截切問題。且因第三胎可能未完整觀察，又有右設限的問題。我們探討分佈的邊界性質，並提出無母數的估計函數。模擬顯示我們的方法具有良好的性質。我們將所提出的方法用於分析孟加拉的資料，比較婦女的生育行為在身處相異的時代與不同地區的差異。有的地區世代改變明顯，有的地區則數十年如一日。

This thesis is motivated by the dataset BDHS (Bangladesh Demographic and Health Survey) which provides information about women’s birth processes in Bangladesh. Our focus is on the joint analysis of two consecutive times to births based on truncated and right censored data. We pay special attention on the boundary conditions which are often neglected but important to obtain an accurate estimator of the truncation probability. We propose nonparametric estimators for estimating the marginal function and the joint function. Simulations show that the proposed estimators have satisfactory performances. We also apply our methods to analyze the BDHS data.

Abstract i
Content I
List of Figures I
List of Table III
Chapter 1 Introduction 1
1.1 Background 1
1.2 Notation 2
1.2.1 Notations and the framework 2
1.2.2 The phenomenon of truncation 3
1.3 Outline 5
Chapter 2 Literature Reviewed 6
2.1 The thesis of Chen (2017) 6
2.2 The thesis of Lee (2018) and our modification 7
Chapter 3 Numeric Analysis 11
3.1 The estimators of and - revisited 11
3.2 Simulation for and 14
3.3 The adjusted estimator of 20
3.4 The adjusted estimator of 22
3.5 Simulation 24
Chapter 4 Data Analysis 29
4.1 BDHS data 29
4.2 Adjusted K-M estimation of Y1 and Y2 32
4.3 Joint analysis of Y1 and Y2 37
4.4 Apply the adjusted 39
Chapter 5 Conclusion 45
References 46

2.2 The thesis of Lee (2018) and our modification 7
Chapter 3 Numeric Analysis 11
3.1 The estimators of and - revisited 11
3.2 Simulation for and 14
3.3 The adjusted estimator of 20
3.4 The adjusted estimator of 22
3.5 Simulation 24
Chapter 4 Data Analysis 29
4.1 BDHS data 29
4.2 Adjusted K-M estimation of Y1 and Y2 32
4.3 Joint analysis of Y1 and Y2 37
4.4 Apply the adjusted 39
Chapter 5 Conclusion 45
References 46

1. CAMPBELL, G. & FOLDES, A. (1982). Large sample properties of nonparametric statistical inference. In Colloquia Methemetica-Societatis, Janos Bolyai, Ed. B. V. Gnedenko, M. L. Puri and I. Vincze, pp. 103-22. Amsterdam: North Holland.
2. LAGAKOS, S. W., BARRAJ, L. M., & Gruttola, V. D. (1988). Nonparametric analysis of truncated survival data, with application to AIDS. Biometrika, 75(3), 515-523.
3. Lin, D. Y., Sun, W., & Ying, Z. (1999). Nonparametric estimation of the gap time distribution for serial events with censored data. Biometrika, 86(1), 59-70.
4. Ling-Yu Li(2018). Statistical Analysis of Recurrent Birth Data Subject to Truncation and Censoring. National Chiao Tung University, Hsinchu, Taiwan.
5. PO-KUEI CHEN (2017). Statistical Analysis for Birth Data based on Retrospective Design. National Chiao Tung University, Hsinchu, Taiwan.
6. Shuyuan He and Grace L. Yang (1998). Estimation of the truncation probability in the random truncation model. The Annals of Statistics Vol. 26, No. 3, 1011–1027
7. Wang, W. and Wells, M. T. 1998. “Nonparametric Estimation of Successive Duration Times under Dependent Censoring,”. Biometrika, 85: 561–572.
8. Woodroofe,M. (1985). Estimating a distribution function with truncated data. Ann. Statist. 13 163–177.