A class of estimators based on overlapping sample spacings

Rahul Singh () and Neeraj Misra
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Rahul Singh: Indian Institute of Technology Kanpur
Neeraj Misra: Indian Institute of Technology Kanpur

Statistical Papers, 2023, vol. 64, issue 6, No 14, 2137-2160

Abstract: Abstract In parametric models, minimising different estimators of the Kullback–Leibler divergence between the empirical distribution function and the true distribution function yield the maximum likelihood estimator (MLE) and the maximum spacings product estimator. This approach has been extended in the literature to minimise some estimators of Csisźar divergence between the empirical distribution function and the true distribution function. Such estimators based on disjoint spacings have recently been studied in the literature. This paper considers analogues of these estimators based on overlapping sample spacings. The estimators have been found to be consistent and asymptotically normally distributed under a broad set of regularity conditions. Asymptotically and for any fixed order of spacings, such estimators are at least as good as the corresponding estimators based on non-overlapping spacings. Simulation studies show that some of these estimators perform better than the MLE for contaminated models. An application to real data reveals that the considered estimators can perform better than the MLE for parsimonious models.

Keywords: Asymptotic normality; Consistency; Estimation; Overlapping sample spacings; Robustness; 62F10; 62F12 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s00362-022-01377-x

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