Fan and Huang (2001) presented a goodness-of-fit test for linear models based on Fourier transformations of the residuals of the fitted model. We present two more theoretically appealing tests in which the Fourier transforms are incorporated into a fitted model. We show that when suitably normalized, the new test statistics have the same asymptotic distribution as Fan and Huang's test. We propose modifications to the asymptotic normalization constants to improve the small sample sizes of our tests while retaining their asymptotic distributions. Small sample sizes and powers are examined via simulations. Real data of short-leaf pines from Bruce and Schumacher (1935) are used to illustrate the performance of the proposed tests.
Level of Degree
Mathematics & Statistics
First Committee Member (Chair)
Second Committee Member
Third Committee Member
Linear models (Statistics), Goodness-of-fit tests, Fourier transformations, Regression analysis--Asymptotic theory, Forests and forestry--Measurement--Statistical methods.
Sun, Siu Kei. "Alternative goodness-of-fit tests for linear models." (2010). http://digitalrepository.unm.edu/math_etds/71