Statistics and Its Interface

Volume 11 (2018)

Number 1

Testing the mean in multivariate regression using set-indexed Gaussian white noise

Pages: 61 – 77



Wayan Somayasa (Department of Mathematics, Halu Oleo University, Kendari, South East Sulawesi, Indonesia)

Herdi Budiman (Department of Mathematics, Halu Oleo University, Kendari, South East Sulawesi, Indonesia)


We propose an asymptotic test method for checking the validity of a multivariate spatial regression that utilizes the distribution model of set-indexed Gaussian white noise. The random set function is obtained as the limit of the partial sums of the vector of observations sampled according to a continuous probability measure (design). It is shown under relatively mild condition that the test which is defined as the integral with respect to the partial sums of the observation converges to an optimal test constructed based on the Cameron–Martin density of the multivariate shifted Gaussian white noise. The optimality of the design under which the experiment was performed is also investigated. We also study the application of the established test procedure to a multivariate real data obtained from a mining industry.


multivariate set-indexed Gaussian white noise, multivariate spatial regression, set-indexed partial sums process, model-check, Cameron–Martin density, signed measure, optimal design

2010 Mathematics Subject Classification

60G10, 60G15, 62G08, 62J05

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This work was supported by the KLN and Publikasi Internasional research fund 2016 provided by the ministry of RISTEK-DIKTI.

Received 22 August 2016

Published 23 August 2017