Goodness-of-fit test with nuisance regression and scale |
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Authors: | Jana Jureková Jan Picek and Pranab Kumar Sen |
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Institution: | (1) no OrgDivision, Charles University, no street, 000, 000 Prague, Czech Republic;(2) no OrgDivision, Technical University of Liberec, no street, 000, 000 no city, Czech Republic;(3) no OrgDivision, University of North Carolina at Chapel Hill, no street, 000, 000 no city, U.S.A. |
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Abstract: | In the linear model Y
i = x
i + e
i, i=1, ,n, with unknown ( , ), ![beta](/content/jj763ve506e8qbkt/xxlarge946.gif) {\open R}p, >0, and with i.i.d. errors e
1, ,e
n having a continuous distribution F, we test for the goodness-of-fit hypothesis H
0:F(e) F
0(e/ ), for a specified symmetric distribution F
0, not necessarily normal. Even the finite sample null distribution of the proposed test criterion is independent of unknown ( , ), and the asymptotic null distribution is normal, as well as the distribution under local (contiguous) alternatives. The proposed tests are consistent against a general class of (nonparametric) alternatives, including the case of F having heavier (or lighter) tails than F
0. A simulation study illustrates a good performance of the tests.
Received July 2001 |
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Keywords: | Contiguity Heavier (lighter) tails Regression quantiles Regression rank scores Regression interquartile range |
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