Asymptotic Theory in Model Diagnostic for General Multivariate Spatial Regression
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, w...
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| Format: | Article |
| Language: | English |
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Wiley
2016-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2016/2601601 |
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| author | Wayan Somayasa Gusti N. Adhi Wibawa La Hamimu La Ode Ngkoimani |
| author_facet | Wayan Somayasa Gusti N. Adhi Wibawa La Hamimu La Ode Ngkoimani |
| author_sort | Wayan Somayasa |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-c41cfca875f94e57b469b7162ddb4047 |
| institution | OA Journals |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2016-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-c41cfca875f94e57b469b7162ddb40472025-08-20T02:18:57ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252016-01-01201610.1155/2016/26016012601601Asymptotic Theory in Model Diagnostic for General Multivariate Spatial RegressionWayan Somayasa0Gusti N. Adhi Wibawa1La Hamimu2La Ode Ngkoimani3Department of Mathematics, Haluoleo University, Kendari, IndonesiaDepartment of Mathematics, Haluoleo University, Kendari, IndonesiaDepartment of Geological Engineering, Haluoleo University, Kendari, IndonesiaDepartment of Geological Engineering, Haluoleo University, Kendari, IndonesiaWe 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.http://dx.doi.org/10.1155/2016/2601601 |
| spellingShingle | Wayan Somayasa Gusti N. Adhi Wibawa La Hamimu La Ode Ngkoimani Asymptotic Theory in Model Diagnostic for General Multivariate Spatial Regression International Journal of Mathematics and Mathematical Sciences |
| title | Asymptotic Theory in Model Diagnostic for General Multivariate Spatial Regression |
| title_full | Asymptotic Theory in Model Diagnostic for General Multivariate Spatial Regression |
| title_fullStr | Asymptotic Theory in Model Diagnostic for General Multivariate Spatial Regression |
| title_full_unstemmed | Asymptotic Theory in Model Diagnostic for General Multivariate Spatial Regression |
| title_short | Asymptotic Theory in Model Diagnostic for General Multivariate Spatial Regression |
| title_sort | asymptotic theory in model diagnostic for general multivariate spatial regression |
| url | http://dx.doi.org/10.1155/2016/2601601 |
| work_keys_str_mv | AT wayansomayasa asymptotictheoryinmodeldiagnosticforgeneralmultivariatespatialregression AT gustinadhiwibawa asymptotictheoryinmodeldiagnosticforgeneralmultivariatespatialregression AT lahamimu asymptotictheoryinmodeldiagnosticforgeneralmultivariatespatialregression AT laodengkoimani asymptotictheoryinmodeldiagnosticforgeneralmultivariatespatialregression |