Rank Based Tests for Testing the Constancy of the Regression Coefficients Against Random Walk Alternatives
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 coefficient...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wrocław University of Science and Technology
2011-01-01
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| Series: | Operations Research and Decisions |
| Online Access: | http://orduser.pwr.wroc.pl/DownloadFile.aspx?aid=1015 |
| Summary: | 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 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 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. (original abstract) |
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| ISSN: | 2081-8858 2391-6060 |