Issue: 2011/Vol.21/No.3-4, Pages 35-55
RANK BASED TESTS FOR TESTING THE CONSTANCY OF THE REGRESSION COEFFICIENTS AGAINST RANDOM WALK ALTERNATIVES
Manohar B. Rajarshi
, Thekke V. Ramanathan, Chanchala A. Ghadge
Cite as: M. B. Rajarshi, T. V. Ramanathan, C. A. Ghadge. Rank based tests for testing the constancy of the regression coefficients against random walk alternatives. Operations Research and Decisions 2011: 21(3-4), 35-55. DOI 10.5277/ord1203-0403
Abstract
A class of approximately locally most powerful type tests based on ranks of residuals is suggest- ed for testing the hypothesis that the regression coefficient is constant in a standard regression model against the alternatives that a random walk process generates the successive regression coefficients. We derive the asymptotic null distribution of such a rank test. This distribution can be described as a generalization of the asymptotic distribution of the Cramer-von Mises test statistic. However, this distribution is quite complex and involves eigen values and eigen functions of a known positive definite kernel, as well as the unknown density function of the error term. It is then natural to apply bootstrap procedures. Extending a result due to Shorack in [25], we have shown that the weighted empirical process of residuals can be bootstrapped, which solves the problem of finding the null dis- tribution of a rank test statistic. A simulation study is reported in order to judge performance of the suggested test statistic and the bootstrap procedure.
Keywords: bootstrap, random coefficient regression models, random walk alternative models, rank tests, weighted empirical and rank processes
Received: Accepted: