臺灣博碩士論文加值系統

當失敗時間T僅在區間[U,V]內時才會出現雙截資料，其中U和V分別是左截時間和右截時間。在本論文中，我們考慮分析具有雙截資料的半參數轉換模型。在文獻中，大多數現有方法都假設失敗時間和截斷時間是獨立的，這在實踐中可能會被違反。為了在給定共變數的情況下將獨立性假設放鬆為條件獨立性，我們考慮模型的回歸參數和累積風險函數的條件最大概似估計量(cMLE)。使用回歸參數和無限維累積函數的score方程，我們提出了一種迭代演算法來獲得cMLE。我們證明cMLE是一致的且漸近常態的。模擬結果顯示，當獨立性假設成立時，cMLE表現得足夠好，並且比現有的估計器表現得更好。

Doubly truncated data occur when a failure time T is observed only if it falls within an interval [U, V ], where U and V are left-truncation and right-truncation times, respectively. In this dissertation, we consider analysis of semiparametric transformation regression models with doubly truncated data. In literature, most of the existing methods assume that failure times and truncation times are independent, which may be violated in practice. To relax the independence assumption to conditional independence given covariates, we consider the conditional maximum likelihood estimators (cMLE) for the regression parameters and cumulative hazard function of models. Using score equations for the regression parameters and the infinite-dimensional cumulative function, we propose an iterative algorithm for obtaining the cMLE. We show that the cMLE is consistent and asymptotically normal. Simulation result demonstrate that the cMLE performs adequately and performs better than the existing estimators when the independence assumption holds.

1 Introduction
1.1 Nonparametric Analysis
1.2 Regression Analysis
2 The Proposed Estimator
2.1 The cMLE
2.2 Computational algorithms for the cMLE
2.3 Asymptotic Properties
3 Simulation Studies
3.1 The cMLE under the dependent case
3.1.1 When both covariates are discrete and U depends on one covariate
3.1.2 When one covariate is continuous and U depends on one covariate
3.1.3 When U depends on two covariates
3.2 Comparison with EM estimator of Rennert and Xie (2018)
3.3 Independent Case
4 Analysis of AIDS Data
5 Discussion
6 Appendix
6.1 Appendix A: Proof of Proposition 1
6.2 Appendix B: Proof of Theorem 1
6.3 Appendix C: Proof of Theorem 2

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