Tests for the equality of conditional variance functions in nonparametric regression
In this paper we are interested in checking whether the conditional variances are equal in k ≥ 2 location-scale regression models. Our procedure is fully nonparametric and is based on the comparison of the error distributions under the null hypothesis of equality of variances and without making use...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2015 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/42212 |
| Acceso en línea: | http://hdl.handle.net/11441/42212 https://doi.org/10.1214/15-EJS1058 |
| Access Level: | acceso abierto |
| Palabra clave: | Asymptotics Bootstrap Comparison of curves Empirical characteristic function Empirical distribution function Kernel smoothing Local alternatives Regression residuals |
| Sumario: | In this paper we are interested in checking whether the conditional variances are equal in k ≥ 2 location-scale regression models. Our procedure is fully nonparametric and is based on the comparison of the error distributions under the null hypothesis of equality of variances and without making use of this null hypothesis. We propose four test statistics based on empirical distribution functions (Kolmogorov-Smirnov and Cramèr-von Mises type test statistics) and two test statistics based on empirical characteristic functions. The limiting distributions of these six test statistics are established under the null hypothesis and under local alternatives. We show how to approximate the critical values using either an estimated version of the asymptotic null distribution or a bootstrap procedure. Simulation studies are conducted to assess the finite sample performance of the proposed tests. We also apply our tests to data on household expenditures. |
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