Testing regression models with residuals as data by Xia Hua.

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.

Department dc:contributor.department

Massachusetts Institute of Technology. Dept. of Mathematics.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2010

Author dc:creator

• Hua, Xia, Ph. D. Massachusetts Institute of Technology

Advisor dc:contributor.advisor

• Richard M. Dudley.

• Mathematics.

Statement dc:rights

• 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.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/60192

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/60192