A DEVIANCE FUNCTION FOR THE QUASI-LIKELIHOOD METHOD
A DEVIANCE FUNCTION FOR THE QUASI-LIKELIHOOD METHOD
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作者：
LI, B
我们引入了一个可以与拟似然方法结合使用的偏差函数。当拟对数似然函数未唯一定义时，就会需要此类函数。通过将一对中心似然比投影到观测值所跨越的两个希尔伯特空间的直接和上来获得偏差。在零假设和备择假设的局部，偏差函数相当于准对数似然比，前提是后者是唯一定义的。与准对数似然比一样，它在观测中是不变的、反对称的和线性的。它可以为独立观察和相关观察定义。在某些情况下，当准得分有多个根时，基于偏差的置信度设置优于基于得分检验的置信度设置。这种偏差还会引起两组矩之间的散度度量，这类似于两个概率度量之间的 Jeffrey 散度。
We introduce a deviance function that can be used in conjunction with the quasi-likelihood method. The need for such functions arises when the quasi-log likelihood function is not uniquely defined. The deviance is obtained by projecting a pair of centred likelihood ratios onto the direct sum of two Hilbert spaces spanned by the observations. Locally at the null and the alternative hypotheses, the deviance function is equivalent to the quasi-log likelihood ratio provided that the latter is uniquely defined. Like the quasi-log likelihood ratio, it is invariant, antisymmetric and linear in the observations. It can be defined for both independent and dependent observations. In certain situations, when the quasi-score has multiple roots, the confidence set based on the deviance is better than that based on the score test. The deviance also induces a divergence measure between two sets of moments, which resembles Jeffreys divergence between two probability measures.