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首页> 外文期刊>IEEE Transactions on Signal Processing >Measure-Transformed Quasi-Maximum Likelihood Estimation
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Measure-Transformed Quasi-Maximum Likelihood Estimation

机译：量度变换的拟最大似然估计

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In this paper, the Gaussian quasi-maximum likelihood estimator (GQMLE) is generalized by applying a transform to the probability distribution of the data. The proposed estimator, called measure-transformed GQMLE (MT-GQMLE), minimizes the empirical Kullback–Leibler divergence between a transformed probability distribution of the data and a hypothesized Gaussian probability measure. By judicious choice of the transform we show that, unlike the GQMLE, the proposed estimator can gain sensitivity to higher order statistical moments and resilience to outliers leading to significant mitigation of the model mismatch effect on the estimates. Under some mild regularity conditions, we show that the MT-GQMLE is consistent, asymptotically normal and unbiased. Furthermore, we derive a necessary and sufficient condition for asymptotic efficiency. A data driven procedure for optimal selection of the measure transformation parameters is developed that minimizes the trace of an empirical estimate of the asymptotic mean-squared-error matrix. The MT-GQMLE is applied to linear regression and source localization and numerical comparisons illustrate its robustness and resilience to outliers.
机译：本文通过对数据的概率分布进行变换来推广高斯拟最大似然估计器（GQMLE）。拟议的估计器称为量度转换GQMLE（MT-GQMLE），它使数据的转换概率分布与假设的高斯概率测度之间的经验Kullback-Leibler差异最小。通过对转换的明智选择，我们表明，与GQMLE不同，拟议的估计器可以提高对高阶统计矩的敏感性，并能抵抗异常值，从而显着减轻模型对估计的失配影响。在一些轻微的规律性条件下，我们显示MT-GQMLE是一致的，渐近正常且无偏见的。此外，我们导出了渐近效率的充要条件。开发了一种数据驱动程序，用于最佳选择量度转换参数，该方法可最大程度地减少对渐进均方误差矩阵的经验估计的痕迹。 MT-GQMLE用于线性回归和源定位，数值比较说明了其鲁棒性和对异常值的适应性。

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