在處理競爭風險的資料時，由於造成特定物件失效的原因有許多種，因此估計特定失效物件的具體-理由分布函數是相當重要的。然而，在面對多維的失效時間時，即使是二維資料其亦具有相當難度。本篇論文中，我們考慮Sankaran 等人在 (2006) 所提出的一種無母數的二維具體-理由分布函數估計量。在此，我們提出一個改善原有方法的一種新的無母數估計量。我們以理論上以及數值上去展示我們的估計量較原有的估計量有更小的均方誤差。我們亦證明此估計量的一致性。針對此估計量的表現我們將進行模擬研究。最後我們把此有效的方法利用到老鼠與蠑螈的資料上並以3D圖來表現其效果。

For competing risks data, it is important to estimate the cause-specific distribution function of a particular failure event, which is the failure probability in the presence of other risks. However, if multiple failure events per subject are available, estimation procedures become challenging, even for the bivariate case. In this thesis, we consider the nonparametric estimation of bivariate cause-specific distribution function which is discussed in Sankaran et al. (2006). In particular, we propose a new nonparametric estimator which improves upon the estimator of Sankaran et al. It is shown theoretically and numerically that the proposed estimator has smaller mean square error than the existing one. The consistency of the proposed estimator is also established. A simulation study is conducted to investigate the performance of the proposed estimator. The usefulness of the method is illustrated by the salamander data and mouse data.

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