The Two-Sample Problem With Regression Errors: An Empirical Process Approach
We describe how to test the null hypothesis that errors from two parametrically specified regression models have the same distribution versus a general alternative. First we obtain the asymptotic properties of test-statistics derived from the difference between the two residual-based empirical distribution functions. Under the null distribution they are not asymptotically distribution free and, hence, a consistent bootstrap procedure is proposed to compute critical values. As an alternative, we describe how to perform the test with statistics based on martingale-transformed empirical processes, which are asymptotically distribution free. Some Monte Carlo experiments are performed to compare the behaviour of all statistics with moderate sample sizes.
|Date of creation:||May 2005|
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|Publication status:||Published by Ivie|
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- Koul, H. L. & Sen, P. K., 1985. "On a Kolmogorov-Smirnov type aligned test in linear regression," Statistics & Probability Letters, Elsevier, vol. 3(3), pages 111-115, June.
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- Winfried Stute, 2002. "Model Checks for Generalized Linear Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 29(3), pages 535-545.
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