A simple test for the parametric form of the variance function in nonparametric regression |
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Authors: | Holger Dette Benjamin Hetzler |
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Institution: | (1) Department of Statistics, University of Glasgow, Glasgow, UK;(2) Department of Statistics, Mangalore University, Mangalore, 574199, Karnataka, India |
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Abstract: | In this paper a new test for the parametric form of the variance function in the common nonparametric regression model is
proposed which is applicable under very weak smoothness assumptions. The new test is based on an empirical process formed
from pseudo residuals, for which weak convergence to a Gaussian process can be established. In the special case of testing
for homoscedasticity the limiting process is essentially a Brownian bridge, such that critical values are easily available.
The new procedure has three main advantages. First, in contrast to many other methods proposed in the literature, it does
not depend directly on a smoothing parameter. Secondly, it can detect local alternatives converging to the null hypothesis
at a rate n
−1/2. Thirdly, in contrast to most of the currently available tests, it does not require strong smoothness assumptions regarding
the regression and variance function. We also present a simulation study and compare the tests with the procedures that are
currently available for this problem and require the same minimal assumptions. |
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Keywords: | |
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