Robust estimation in functional comparative calibration models via maximum Lq-likelihood

IF 0.6 4区 数学 Q4 STATISTICS & PROBABILITY
Patricia Giménez, Lucas Guarracino, M. Galea
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引用次数: 0

Abstract

. A fully parametric estimation procedure is proposed for robust estimation of the structural parameter in a functional comparative calibration model, under normality. The proposed estimator is obtained, based on maximum L q -likelihood approach, first re-placing the incidental parameters by estimators depending on the structural parameter. The estimator, called ML q E, depends on a single distortion parameter q , which controls the bal-ance between robustness and efficiency. If q tends to 1, the maximum likelihood estimator (MLE) is obtained. The estimation procedure can be implemented easily by a simple and fast re-weighting algorithm. For applying the method to practical and real-data scenarios, a data-based choice of an appropriate value of q is proposed. Consistency and asymptotic normality is established and the covariance matrix is given. The influence function is derived, to show the local robustness properties. Theoretical properties, ease of imple-mentabiliy and empirical results on simulated and real data show the satisfactory behavior of the ML q E and its vantages over the MLE in presence of observations discordant with the assumed model.
基于最大Lq似然的函数比较校准模型的鲁棒估计
. 提出了一种全参数估计方法,用于功能比较校准模型在正态性下的结构参数的鲁棒估计。基于最大lq似然方法,首先用基于结构参数的估计量替换偶然参数,得到了所提出的估计量。估计器,称为ML q E,依赖于一个单一的失真参数q,它控制鲁棒性和效率之间的平衡。如果q趋于1,则得到极大似然估计量(MLE)。该估计过程可以通过一种简单快速的重加权算法轻松实现。为了将该方法应用于实际和真实数据场景,提出了基于数据选择适当q值的方法。建立了一致性和渐近正态性,给出了协方差矩阵。推导了影响函数,证明了该方法的局部鲁棒性。理论性质、易实现性以及模拟和实际数据的经验结果表明,ML q E具有令人满意的性能,并且在与假设模型不一致的观测值存在时,它优于MLE。
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来源期刊
CiteScore
1.60
自引率
10.00%
发文量
30
审稿时长
>12 weeks
期刊介绍: The Brazilian Journal of Probability and Statistics aims to publish high quality research papers in applied probability, applied statistics, computational statistics, mathematical statistics, probability theory and stochastic processes. More specifically, the following types of contributions will be considered: (i) Original articles dealing with methodological developments, comparison of competing techniques or their computational aspects. (ii) Original articles developing theoretical results. (iii) Articles that contain novel applications of existing methodologies to practical problems. For these papers the focus is in the importance and originality of the applied problem, as well as, applications of the best available methodologies to solve it. (iv) Survey articles containing a thorough coverage of topics of broad interest to probability and statistics. The journal will occasionally publish book reviews, invited papers and essays on the teaching of statistics.
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