如何利用樣本觀察值來估計母體參數一直是統計學家感興趣的重要的課題之一，雖然最大概似法與動差法在統計界被廣泛利用，但還是有其缺陷，像是Cauchy分配並無法使用這兩種估計法來估計母體參數，因此本文透過最小距離的概念提出幾何估計法，不僅適用於完整資料的母體參數估計，當實驗數據為設限資料時也能夠利用幾何估計法來估計母體參數，並且進一步利用幾何估計法來估計比例風險模型中的參數。藉由電腦模擬與傳統估計方法比較，幾何估計法在變異數以及均方誤差都有較佳的表現。

Statisticians are always interested in how to use sample statistics to estimate population parameters. Both maximum likelihood estimation (MLE) and method of moments (MOM) are the most popularly used in the statistical field, but they each have their own drawbacks. For instance, these two methods cannot be applied to parameter estimation of the Cauchy distribution. This paper propose a geometric approach to estimation that is based on the concept of the minimum distance. It can be used to estimate not only the distribution parameters with complete and censored data but also parameters in Cox’s proportional hazards model. Computer simulation results show that the new method has a great improvement in variance and mean squared error on the traditional methods.

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