http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
application of Fourier series smoothing to a diagnostic test of heterocedasticity
A test for heteroscedasticity in linear and nonparametric
regression problems is proposed. The test is based on
smoothing the residual plot and is an adaptation of the test
for "no effect" of Eubank and Hart (1992). A major advantage
of the proposed test is that its assumptions about the
alternative to homoscedasticity are reduced to requiring that
the variance be a piecewise smooth function of some known
variable. Additionally, if homoscedasticity is rejected, the
test produces a direct estimate of the variance function.
The asymptotic null distribution of the test statistic is
derived, and the test is shown to be consistent and able to
detect local alternatives converging to the null at the rate
n-1/2. Based on simulation studies, the test is shown to
have reasonable power compared to the parametric test of Cook
and Weisberg (1983), when the alternative is of the form
specified by the parametric test, and can have power far
superior to the parametric test when the alternative is
misspecified. It is also shown that for moderate to large
sample sizes the test performs better than the nonparametric
test based on the rank correlation proposed by Yin and
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Includes bibliographical references: pages 82-85.