Empirical bias-reducing adjustments to estimating functions
Empirical bias-reducing adjustments to estimating functions
复制标题
对估计函数进行经验偏差减少调整
DOI：
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复制
发表时间：
2020
期刊：
影响因子：
--
通讯作者：
N. Lunardon
中科院分区：
文献类型：
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作者：
I. Kosmidis;N. Lunardon
我们开发了一种新颖的通用框架，用于根据渐近无偏估计函数进行减少偏差 $M$ 估计。该框架依赖于估计函数贡献的导数函数对偏差的经验近似。减少偏差 $M$ 估计可以通过求解经验调整的估计方程来隐式运行，也可以通过从原始 $M$ 估计中减去估计偏差来显式运行，并适用于部分或完全指定的模型，具有可能性或其他替代目标。自动微分可用于抽象出实现减少偏差 $M$ 估计所需的唯一代数。因此，与其他需要对对数似然导数乘积的期望进行重采样或评估的已建立的偏差减少方法相比，我们引入的偏差减少方法具有明显更广泛的适用性和更直接的实施。如果$M$-估计是通过最大化一个目标，那么总是存在一个减少偏差的惩罚目标。该惩罚目标与模型选择的信息标准密切相关，并且可以通过插件惩罚进一步增强，以提供具有额外属性的减少偏差 $M$ 估计，例如分类数据模型的有限性。减少偏差的 $M$ 估计量与原始 $M$ 估计量具有相同的渐近分布，因此，推理和模型选择的标准程序不会因改进的估计而改变。我们在不同复杂度的常用、突出的建模设置中演示和评估减少偏差 $M$ 估计的属性。
We develop a novel, general framework for reduced-bias $M$-estimation from asymptotically unbiased estimating functions. The framework relies on an empirical approximation of the bias by a function of derivatives of estimating function contributions. Reduced-bias $M$-estimation operates either implicitly, by solving empirically adjusted estimating equations, or explicitly, by subtracting the estimated bias from the original $M$-estimates, and applies to models that are partially- or fully-specified, with either likelihoods or other surrogate objectives. Automatic differentiation can be used to abstract away the only algebra required to implement reduced-bias $M$-estimation. As a result, the bias reduction methods we introduce have markedly broader applicability and more straightforward implementation than other established bias-reduction methods that require resampling or evaluation of expectations of products of log-likelihood derivatives. If $M$-estimation is by maximizing an objective, then there always exists a bias-reducing penalized objective. That penalized objective relates closely to information criteria for model selection, and can be further enhanced with plug-in penalties to deliver reduced-bias $M$-estimates with extra properties, like finiteness in models for categorical data. The reduced-bias $M$-estimators have the same asymptotic distribution as the original $M$-estimators, and, hence, standard procedures for inference and model selection apply unaltered with the improved estimates. We demonstrate and assess the properties of reduced-bias $M$-estimation in well-used, prominent modelling settings of varying complexity.
影响因子：
2.7
作者：
Kosmidis, Ioannis;Firth, David
通讯作者：
Firth, David
影响因子：
1.1
作者：
Kosmidis, Ioannis;Firth, David
通讯作者：
Firth, David