2026-09-19T18:09:21Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/601922022-01-13T07:54:35Zcom_1721.1_7582com_1721.1_7581col_1721.1_131022
Richard M. Dudley.
Hua, Xia, Ph. D. Massachusetts Institute of Technology
Massachusetts Institute of Technology. Dept. of Mathematics.
Massachusetts Institute of Technology. Department of Mathematics
2010-12-06T17:36:06Z
2010-12-06T17:36:06Z
2010
2010
http://hdl.handle.net/1721.1/60192
681920612
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2010.
Cataloged from PDF version of thesis.
Includes bibliographical references (p. 85-86).
Abstract In polynomial regression ... . In this thesis, I developed a residual based test, the turning point test for residuals, which tests the hypothesis that the kth order polynomial regression holds with ... while the alternative can simply be the negation or be more specific, e.g., polynomial regression with order higher than k. This test extends the rather well known turning point test and requires approximation of residuals by errors for large n. The simple linear regression model, namely k = 1, will be studied in most detail. It is proved that the expected absolute difference of numbers of turning points in the errors and residuals cannot become large and under mild conditions becomes small at given rates for large n. The power of the test is then compared with another residual based test, the convexity point test, using simulations. The turning point test is shown to be more powerful against quadratic alternatives.
Ph.D.
86 p.
eng
Massachusetts Institute of Technology
M.I.T. theses are protected by
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http://dspace.mit.edu/handle/1721.1/7582
Mathematics.
Testing regression models with residuals as data by Xia Hua.
Thesis
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