Recursive Residuals Partial Sums Method for Testing Model Validity in Modelling of Spatial Data

摘要

The main objective of this work is to model spatial observations using linear regression analysis defined on a compact experimental region. To check the validity of an assumed model, tests based on Kologorov-Smirnov and Cramer-von Mises functionals of the partial sums (CUSUM) of the recursive residuals of the observations are proposed. It is shown that the limit of the sequence of the CUSUM processes of the recursive residuals for triangular array of design points does not depend on the model. It is given by the set-indexed Brownian sheet when the model is true. The performance of the tests are also studied by deriving the non trivial limiting power functions of the tests when the model is not true. Their finite sample size behaviors are compared with those of the well-known asymptotic F test and are investigated by simulation. It is shown in this study that both Cramer-von Mises and F tests perform better than the Kolmogorov-Smirnov test. The application of the proposed method in a real data is also exhibited. The design under which the data has been collected is given by a regular lattice.