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Wayan Somayasa



Authors and WSEAS

Wayan Somayasa


WSEAS Transactions on Mathematics


Print ISSN: 1109-2769
E-ISSN: 2224-2880

Volume 18, 2019

Notice: As of 2014 and for the forthcoming years, the publication frequency/periodicity of WSEAS Journals is adapted to the 'continuously updated' model. What this means is that instead of being separated into issues, new papers will be added on a continuous basis, allowing a more regular flow and shorter publication times. The papers will appear in reverse order, therefore the most recent one will be on top.


Volume 18, 2019



Multivariate Recursive Residuals Partial Sums Processes and Its Application in Model Check for Multiresponse Regression

AUTHORS: Wayan Somayasa

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In this paper asymptotic test in multivariate regression based on set-indexed partial sums of the vector of recursive residuals is proposed. The limit process is derived for multivariate nonparametric regression with localized vector of regression functions under an equally spaced experimental design on a closed rectangle. Under mild condition it is shown that independent to the assumed model, the partial sums processes converges to a vector of trends plus the multivariate set-indexed Brownian sheet. The trend vanishes simultaneously when the hypothesis is true living the multivariate set-indexed Brownian sheet as the only limit process. The finite sample size behavior of the power functions of Kolmogorov-Smirnov (KS) and Cramer-von Mises (CM) type tests are investigated by ´ simulation. It is shown that for testing multivariate polynomial model of low order the CM test seems to have larger power than the KS test has. The application of the test method in the empirical model building of corn plants data and its comparison with the classical test using Wilk’s lambda statistic is also demonstrated

KEYWORDS: multivariate linear regression, recursive residual, least squares residuals, partial sums process, multivariate Brownian sheet, Kolmogorov-Smirnov test, Cramer-von Mises test, Wilk’s lambda

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[16] W. Somayasa and G.N.A. Wibawa, Asymptotic model-check for multivariate spatial regression with correlated responses Fareast J. Math. Sci. 98(5), 2015, pp. 613–939. WSEAS TRANSACTIONS on MATHEMATICS Wayan Somayasa E-ISSN: 2224-2880 337 Volume 18, 2019

[17] W. Somayasa, G.N.A. Wibawa, and Y.B. Pasolon, Multidimensional Set-Indexed Partial Sums Method for Checking the Appropriateness of a Multivariate Spatial Regression Int. J. Math. Models and Methods in Applied Sciences, 9, 2015, pp. 700-713.

[18] W. Somayasa, G.N.A. Wibawa, L. Hamimu and L.O. Ngkoimani, Asymptotic theory in model diagnostic for general multivariate spatial regression, Int. J. Mathematics and Mathematical Sciences 2016, pp. 1–16.

[19] W. Somayasa, Estimating the power of lack-offit test for the mean of multivariate spatial regression, Applied Mathematical Sciences, 11(52), 2017, pp. 2587–2607.

[20] W. Somayasa, Accessing the Power of Tests Based on Set-Indexed Partial Sums of Multivariate Regression Residuals, Journal of Applied Mathematics, 2018, pp. 1–13

[21] W. Somayasa, Recursive residuals partial sums method for testing model validity in modelling of spatial data, WSEAS Trans. Math., 18, 2019, pp. 62–72.

[22] L. Xie and I.B. MacNeill, Spatial residual processes and boundary detection, South African Statist. J. 4, 2006, pp. 33–53.

WSEAS Transactions on Mathematics, ISSN / E-ISSN: 1109-2769 / 2224-2880, Volume 18, 2019, Art. #41, pp. 326-338


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