Saddlepoint approximations for the distribution of some robust estimators of the variogram

A. García-Pérez ()
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A. García-Pérez: Universidad Nacional de Educación a Distancia (UNED)

Metrika: International Journal for Theoretical and Applied Statistics, 2020, vol. 83, issue 1, No 4, 69-91

Abstract: Abstract In this paper, we obtain a saddlepoint approximation for the small sample distribution of several variogram estimators such as the classical Matheron’s estimator, some M-estimators like the robust Huber’s variogram estimator, and also the $$\alpha $$α-trimmed variogram estimator. The tail probability approximation obtained is very accurate even for small sample sizes. In the approximations we consider that the observations follow a distribution close to the normal, specifically, a scale contaminated normal model. To obtain the approximations we transform the original observations into a new ones, which can be considered independent if a linearized variogram can be accepted as model for them. To check this, a goodness of fit test for a variogram model is defined in the last part of the paper.

Keywords: Robustness; Spatial data; Saddlepoint approximation; 62F35; 62H11; 62E17 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s00184-019-00725-6

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