在本篇論文中，我們探討左截切及右設限資料型態的分量迴歸分析，分量迴歸模型可以提供我們在偏態分佈下，任何分量的解釋變數效果。我們利用IPCW的技巧去獲得解釋變數效果的估計，並提供所建議估計量的大樣本性質，也提供了模型診斷以及模型選取的方法。我們也藉由模擬實驗來驗証我們所提出的估計式及模型診斷方法。最後應用我們的方法分析一筆退休社區的真實資料來做描述。

In this paper, we consider quantile regression for the left truncated and right censored data. Quantile regression provides the covariate effect for any quantile,which is more appropriate for skew distribution.We use the inverse probability censoring weight (IPCW) technique to obtain estimates of effects of explanatory variables, and provide the large sample properties of the suggested estimator.We also provide an approach for model diagnostic and model selection.We examine the performance of the proposed estimator and model diagnostic method via simulations.Finally, we also apply our method to a real data which is Channing House Data for illustration.

1 Introduction 1
2 Literature Review 3
2.1 A Proportional Hazards Regression Model for the Subdistri-
bution with Right Censored and Left Truncated Competing
Risks Data (Xu Zhang, Mei-Jie Zhang and Jason P. Fine, 2011) 3
2.2 Competing Risks Quantile Regression (Peng and Fine, 2009) . 6
3 The Proposed Inference Procedure 9
3.1 Data and Notations . . . . . . . . . . . . . . . . . . . . . . . . 9
3.2 Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
3.3 The Estimating Equation of βτ . . . . . . . . . . . . . . . . . 12
3.4 Large Sample Properties . . . . . . . . . . . . . . . . . . . . . 14
3.5 Estimation of Variance and Covariance . . . . . . . . . . . . . 16
4 Model Checking and Model Diagnosis 18
5 Simulation Studies 20
6 Real Data Analysis 38
7 Concluding Remarks 41
References 43
Appendix A: The Relationship between Sn (b, τ) and Un (b, τ) 46
Appendix B: Proof of Theorem 1 47
Appendix C: Proof of Theorem 2 51

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