Accessing the Appropriateness of a Spatial Regression Using Generalized (<i>h</i>₁<i>h</i>₂-)Slepian Random Field

Abstract

Abstract:In this study we derived asymptotic goodness-of-fit test (model check) for spatial regression where the critical region as well as the pvalue of the tests are approximated based on the distribution of a type of the integral functional of the generalized (h 1 h 2 -)-Slepian field and the setindexed 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.

Estimating the power of lack-of-fit test for the mean of multivariate spatial regression

“…See the asymptotic test procedures proposed in [18,19,20] for the technical details. The experiment was conducted under an experimental design constructed according to an algorithm proposed in Somayasa [17] and Somayasa and et al [21]. A regularly spaced (equidistance) design which is frequently called a regular lattice is commonly used in the practice.…”