Paper Info
Title
Measure-Transformed Quasi Maximum Likelihood Estimation
Abstract
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 signal gain estimation and source localization and numerical comparisons illustrate its robustness and resilience to outliers.
Year
Venue
Field
2017
IEEE Trans. Signal Processing
Econometrics,Likelihood function,Estimation of covariance matrices,Probability measure,Uniform distribution (continuous),Empirical probability,Exponential distribution,Estimation theory,Statistics,Mathematics,Estimator
DocType
Volume
Issue
Journal
65
3
Citations 
PageRank 
References 
4
0.50
15
Authors
2
Name
Order
Citations
PageRank
Koby Todros19411.35
Alfred O. Hero III22600301.12