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最大似然估计的中位数偏差校正AI 解读

For regular parametric problems, we show how median centring of the maximum likelihood estimate can be achieved by a simple modification of the score equation. For a scalar parameter of interest, the estimator is equivariant under interest-respecting reparameterizations and is third-order median unbiased. With a vector parameter of interest, componentwise equivariance and third-order median centring are obtained. Like the implicit method of Firth (1993) for bias reduction,…

含大量干扰参数模型中的定向修正剖面似然AI 解读

The modified profile likelihood is a higher-order approximation to a conditional or a marginal likelihood, when either exists. The directed likelihood based on the modified profile likelihood is standard normal only to first order. In practice, however, it usually achieves most of the distributional improvement obtained by higher-order methods. This note elucidates this point with particular attention to models with many nuisance parameters.