A test for the parametric form of the variance function in a partial linear regression model
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Date
2007-09-05T12:46:49Z
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Abstract
We consider the problem of testing for a parametric form of the variance function in a
partial linear regression model. A new test is derived, which can detect local alternatives
converging to the null hypothesis at a rate n-1/2 and is based on a stochastic process of the
integrated variance function. We establish weak convergence to a Gaussian process under the
null hypothesis, fixed and local alternatives. In the special case of testing for homoscedasticity
the limiting process is a scaled Brownian bridge. We also compare the finite sample properties
with a test based on an L2-distance, which was recently proposed by You and Chen (2005).
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Keywords
Homoscedasticity, Limiting process, Parametric form, Partial linear regression model, Scaled Brownian bridge, Testing