Research Article Open Access

Accessing the Appropriateness of a Spatial Regression Using Generalized (h1h2-)Slepian Random Field

Wayan Somayasa1, Jamhir Safani1, La Ode Ngkoimani1 and Muhamad Zamrun F.1
  • 1 Halu Oleo University, Indonesia

Abstract

In this study we derived asymptotic goodness-of-fit test (model check) for spatial regression where the critical region as well as the p-value of the tests are approximated based on the distribution of a type of the integral functional of the generalized (h1h2-)-Slepian field and the set-indexed Gaussian white noise. Such random fields are obtained as the limit process of the moving and the cumulative sums processes of the sequence of random matrices consist of independent and identically distributed random variables indexed by the points of a design constructed by means of a given continuous probability measure. Although the common approach in model diagnostic for regression is based on the functional of the residuals, in this study a new different idea is proposed by directly investigating the moving and the cumulative sums of the array of the observations. It is shown that these approaches are mathematically tractable and practically more applicable. Simulation study is conducted for investigating the finite sample size behavior of the tests. An application of the procedure to a mining data is also discussed, where from the perspective of geology and geophysics, polynomial model is reasonable and suitable for the data.

Journal of Mathematics and Statistics
Volume 13 No. 2, 2017, 106-126

DOI: https://doi.org/10.3844/jmssp.2017.106.126

Submitted On: 13 March 2017 Published On: 2 May 2017

How to Cite: Somayasa, W., Safani, J., Ngkoimani, L. O. & F., M. Z. (2017). Accessing the Appropriateness of a Spatial Regression Using Generalized (h1h2-)Slepian Random Field. Journal of Mathematics and Statistics, 13(2), 106-126. https://doi.org/10.3844/jmssp.2017.106.126

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Keywords

  • Slepian Field
  • Set-Indexed White Noise
  • Goodness-of-Fit Test
  • Moving Sum Process
  • Spatial Regression