M-Estimations of Shape and Scale Parameters by Order Statistics in Least Informative Distributions on q-deformed logarithm

Öz

The maximum logq likelihood estimation (MLqE) method is used to estimate robustly parameters recently. In robust estimation method, the least informative distribution (LID) proposed by Huber is a convex combination of two probability density functions 𝑓0 and 𝑓1. In this study, the recently proposed least informative distributions (LIDs) in MLqE are used to estimate parameters. This paper also studies on the objective functions proposed by maximum logq-likelihood principle (MLqE) originally derived by logq-likelihood. The role and capability of order statistics in LIDs in MLqE are examined while getting the estimates of shape and scale parameters. The distance measure for evaluation of fitting performance is given to choose a value for the parameter 𝑞 in logq when the objective functions derived from MLqE are used. The simulation and real data application are given. Thus, we compare the fitting performance of objective functions constructed by MLE on log, MLqE on logq and LIDs with order statistics in MLqE. We observed that order statistic chosen for density 𝑓1 in LID in MLqE has a new objective function to fit the data sets. In the simulation, we make two contaminations into artificial data sets. The first contamination is inliers derived by order statistics and the second one is outliers. Thus, we observe that the new objective function can give satisfactory results.

Anahtar Kelimeler

• Distribution
• efficiency
• estimation
• order statistics
• robustness

Kaynakça

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