When the null hypothesis constrains parameters to the boundary of the parameter space, the asymptotic null distribution of the composite likelihood ratio statistic is often a mixture of weighted chi‐squared distributions. The mixing weights depend on the true unknown parameter and can be very difficult to calculate, except in a few special cases. We propose a Monte Carlo algorithm to estimate the mixing weights through a projection method. We then show how this algorithm facilitates composite likelihood ratio testing under nonstandard conditions.

中文翻译：

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使用切线锥在非标准条件下进行复合似然比测试

当零假设将参数约束到参数空间的边界时，复合似然比统计量的渐近零分布通常是加权卡方分布的混合。混合权重取决于真实的未知参数，除了少数特殊情况外，计算起来可能非常困难。我们提出了一种蒙特卡洛算法，通过投影方法来估计混合权重。然后，我们将展示该算法如何促进非标准条件下的复合似然比测试。