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1 Operations Research and Decisions

1 2011

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Rank based tests for testing the constancy of the regression coefficients against random walk alternatives

Rajarshi M. B., Ramanathan T. V., Ghadge C. A.

Operations Research and Decisions

2011

Vol. 21, No. 3-4

35-55

A class of approximately locally most powerful type tests based on ranks of residuals is suggested 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 coe?cients. 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 defnite 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 distribution of a rank test statistic. A simulation study is reported in order to judge performance of the suggested test statistic and the bootstrap procedure.