平衡增加的经验欧氏似然

经验(欧氏)似然方法是近年来非常流行的一种非参数统计方法.针对经验(欧氏)似然的凸包限制和计算复杂问题,本文借助Emerson和Owen (2009)所提出的平衡增加思想对经验欧氏似然进行修正,得到了平衡增加的经验欧氏似然.随后论文从理论和模拟两个方面进行了研究.理论上给出了该方法与经验欧氏似然检验函数之间的联系,即在固定的样本量n下随着添加点位置的连续变化,检验方法可以从简单的均值增加经验欧氏似然变化到经验欧氏似然检验;模拟结果显示,适当选取调整因子,平衡增加的经验欧氏似然相对于(调整)经验欧氏似然而言,在大多数情况下,其分布更接近于对应的极限分布.

Balanced Augmented Empirical Euclidean Likelihood

Empirical (Euclidean) likelihood is a very popular nonparametric statistical method in recent years. In view of the convex hull restrictions and complex calculation of empirical (Euclidean) likelihood, the balanced augmented empirical Euclidean likelihood (BAEEL) is proposed by using the idea of Emerson and Owen (2009). Then the BAEEL method is investigated from two aspects of theory and simulation. In theory, the connection between BAEEL method and the empirical Euclidean likelihood method is deduced. That is, with fixed sample size and the continuous varied location of augmented points, the test can be varied from the simple mean augmented empirical Euclidean likelihood to empirical Euclidean likelihood test. Simulation results show that the distribution of the BAEEL converges its limit distribution more rapidly than that of the (adjusted) empirical Euclidean likelihood in most cases.