论文标题
具有奇异性和边界模型的广义AIC
A generalized AIC for models with singularities and boundaries
论文作者
论文摘要
Akaike信息标准（AIC）是进行模型选择的常见工具。它经常用于违反参数空间奇点和边界处的规律性条件。预期的AIC通常在奇异性和边界上渐近地等同于其目标，而在附近参数点上与目标的收敛可能很慢。我们为具有或没有奇异性和边界的候选模型开发了广义的AIC。我们表明，这种广义形式的期望在参数空间中无处不在，并且其收敛性可以比AIC的收敛更快。我们说明了从系统基础学中的示例模型上的广义AIC，表明它可以胜过AIC并产生插值有效数量的模型参数，这可能与近似和边界附近的参数数量有很大差异。我们概述了估计广义AIC的通常未知的生成参数和偏置校正项的方法。
The Akaike information criterion (AIC) is a common tool for model selection. It is frequently used in violation of regularity conditions at parameter space singularities and boundaries. The expected AIC is generally not asymptotically equivalent to its target at singularities and boundaries, and convergence to the target at nearby parameter points may be slow. We develop a generalized AIC for candidate models with or without singularities and boundaries. We show that the expectation of this generalized form converges everywhere in the parameter space, and its convergence can be faster than that of the AIC. We illustrate the generalized AIC on example models from phylogenomics, showing that it can outperform the AIC and gives rise to an interpolated effective number of model parameters, which can differ substantially from the number of parameters near singularities and boundaries. We outline methods for estimating the often unknown generating parameter and bias correction term of the generalized AIC.
