Testing regression models with residuals as data by Xia Hua.
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2010.
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| Format: | Thesis |
| Language: | eng |
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Massachusetts Institute of Technology
2010
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| Online Access: | http://hdl.handle.net/1721.1/60192 |
| _version_ | 1826192671854559232 |
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| author | Hua, Xia, Ph. D. Massachusetts Institute of Technology |
| author2 | Richard M. Dudley. |
| author_facet | Richard M. Dudley. Hua, Xia, Ph. D. Massachusetts Institute of Technology |
| author_sort | Hua, Xia, Ph. D. Massachusetts Institute of Technology |
| collection | MIT |
| description | Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2010. |
| first_indexed | 2024-09-23T09:27:10Z |
| format | Thesis |
| id | mit-1721.1/60192 |
| institution | Massachusetts Institute of Technology |
| language | eng |
| last_indexed | 2024-09-23T09:27:10Z |
| publishDate | 2010 |
| publisher | Massachusetts Institute of Technology |
| record_format | dspace |
| spelling | mit-1721.1/601922019-04-12T11:37:35Z Testing regression models with residuals as data by Xia Hua. Hua, Xia, Ph. D. Massachusetts Institute of Technology Richard M. Dudley. Massachusetts Institute of Technology. Dept. of Mathematics. Massachusetts Institute of Technology. Dept. of Mathematics. Mathematics. 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. 2010-12-06T17:36:06Z 2010-12-06T17:36:06Z 2010 2010 Thesis http://hdl.handle.net/1721.1/60192 681920612 eng M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission. http://dspace.mit.edu/handle/1721.1/7582 86 p. application/pdf Massachusetts Institute of Technology |
| spellingShingle | Mathematics. Hua, Xia, Ph. D. Massachusetts Institute of Technology Testing regression models with residuals as data by Xia Hua. |
| title | Testing regression models with residuals as data by Xia Hua. |
| title_full | Testing regression models with residuals as data by Xia Hua. |
| title_fullStr | Testing regression models with residuals as data by Xia Hua. |
| title_full_unstemmed | Testing regression models with residuals as data by Xia Hua. |
| title_short | Testing regression models with residuals as data by Xia Hua. |
| title_sort | testing regression models with residuals as data by xia hua |
| topic | Mathematics. |
| url | http://hdl.handle.net/1721.1/60192 |
| work_keys_str_mv | AT huaxiaphdmassachusettsinstituteoftechnology testingregressionmodelswithresidualsasdatabyxiahua |