A new test for the parametric form of the variance function in non-parametric regression
(2007) Royal Statistical Society. Journal. Series B: Statistical Methodology — Vol. 69, p. 903-917 (2007)
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- Abstract
- In the common non-parametric regression model the problem of testing for the parametric form of the conditional variance is considered. A stochastic process based on the difference between the empirical processes that are obtained from the standardized non-parametric residuals under the null hypothesis (of a specific parametric form of the variance function) and the alternative is introduced and its weak convergence established. This result is used for the construction of a Kolmogorov-Smimov and a Cramer-von Mises type of statistic for testing the parametric form of the conditional variance. The consistency of a bootstrap approximation is established, and the finite sample properties of this approximation are investigated by means of a simulation study. In particular the new procedure is compared with some of the currently available methods for this problem.
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Citations
Dette, H., Neurneyer, N., & Van Keilegom, I. (2007). A new test for the parametric form of the variance function in non-parametric regression. Royal Statistical Society. Journal. Series B: Statistical Methodology, 69, 903-917. https://doi.org/10.1111/j.1467-9868.2007.00616.x (Original work published 2007)