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

Author

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  • A. García-Pérez

    (Universidad Nacional de Educación a Distancia (UNED))

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.

Suggested Citation

  • A. García-Pérez, 2020. "Saddlepoint approximations for the distribution of some robust estimators of the variogram," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 83(1), pages 69-91, January.
    • Handle: RePEc:spr:metrik:v:83:y:2020:i:1:d:10.1007_s00184-019-00725-6
    DOI: 10.1007/s00184-019-00725-6
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    References listed on IDEAS

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    1. Ali, Mukhtar M, 1987. "Durbin-Watson and Generalized Durbin-Watson Tests for Autocorrelations and Randomness," Journal of Business & Economic Statistics, American Statistical Association, vol. 5(2), pages 195-203, April.
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