We examine a higher order approximation to the significance function with increasing numbers of nuisance parameters, based on the normal approximation to an adjusted log‐likelihood root. We show that the rate of the correction for nuisance parameters is larger than the correction for non‐normality, when the parameter dimension p is O(n^α) for $\alpha <\frac{1}{2}$. We specialize the results to linear exponential families and location–scale families and illustrate these with simulations.

中文翻译：

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高维的修正似然根

我们基于对调整后的对数似然根的正态近似，检验了随着扰动参数数量增加而对显着性函数的高阶近似。我们表明，校正为多余参数的速度比校正非正态较大，当参数尺寸p是ø（Ñ ^α），用于$\alpha <\frac{\mathrm{1个}}{2}$。我们将结果专门用于线性指数族和位置尺度族，并通过仿真进行说明。