Testing regression models with residuals as data by Xia Hua.
Name
681920612-MIT.pdf
Description
Full printable version
Size
3.41 MB
Format
Adobe PDF
Checksum (MD5)
dd503fcd91c6e0cee3dc12547d5cd63e
Author(s)
Hua, Xia, Ph. D. Massachusetts Institute of Technology
Advisor(s)
Richard M. Dudley.
Date Issued
2010
Publisher
Massachusetts Institute of Technology
Abstract
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.
Description
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2010.
Cataloged from PDF version of thesis.
Includes bibliographical references (p. 85-86).
Subjects
Mathematics.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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