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Asymptotic Theory in Model Diagnostic for General Multivariate Spatial Regression

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Listed:
  • Wayan Somayasa
  • Gusti N. Adhi Wibawa
  • La Hamimu
  • La Ode Ngkoimani

Abstract

We establish an asymptotic approach for checking the appropriateness of an assumed multivariate spatial regression model by considering the set-indexed partial sums process of the least squares residuals of the vector of observations. In this work, we assume that the components of the observation, whose mean is generated by a certain basis, are correlated. By this reason we need more effort in deriving the results. To get the limit process we apply the multivariate analog of the well-known Prohorov’s theorem. To test the hypothesis we define tests which are given by Kolmogorov-Smirnov (KS) and Cramér-von Mises (CvM) functionals of the partial sums processes. The calibration of the probability distribution of the tests is conducted by proposing bootstrap resampling technique based on the residuals. We studied the finite sample size performance of the KS and CvM tests by simulation. The application of the proposed test procedure to real data is also discussed.

Suggested Citation

  • Wayan Somayasa & Gusti N. Adhi Wibawa & La Hamimu & La Ode Ngkoimani, 2016. "Asymptotic Theory in Model Diagnostic for General Multivariate Spatial Regression," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2016, pages 1-16, September.
    • Handle: RePEc:hin:jijmms:2601601
    DOI: 10.1155/2016/2601601
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    References listed on IDEAS

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    1. Bischoff, Wolfgang & Somayasa, Wayan, 2009. "The limit of the partial sums process of spatial least squares residuals," Journal of Multivariate Analysis, Elsevier, vol. 100(10), pages 2167-2177, November.
    2. Arnold, Steven, 1984. "The asymptotic validity of invariant procedures for the repeated measures model and multivariate linear model," Journal of Multivariate Analysis, Elsevier, vol. 15(3), pages 325-335, December.
    3. Bischoff, W. & Gegg, A., 2011. "Partial sum process to check regression models with multiple correlated response: With an application for testing a change-point in profile data," Journal of Multivariate Analysis, Elsevier, vol. 102(2), pages 281-291, February.
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