Asymptotic refinements of bootstrap tests in a linear regression model ; A CHM bootstrap using the first four moments of the residuals
AbstractWe consider linear regression models and we suppose that disturbances are either Gaussian or non Gaussian. Then, by using Edgeworth expansions, we compute the exact errors in the rejection probability (ERPs) for all one-restriction tests (asymptotic and bootstrap) which can occur in these linear models. More precisely, we show that the ERP is the same for the asymptotic test as for the classical parametric bootstrap test it is based on as soon as the third cumulant is nonnul. On the other side, the non parametric bootstrap performs almost always better than the parametric bootstrap. There are two exceptions. The first occurs when the third and fourth cumulants are null, in this case parametric and non parametric bootstrap provide exactly the same ERPs, the second occurs when we perform a t-test or its associated bootstrap (parametric or not) in the models y =μ+u and y=ax+u where the disturbances have nonnull kurtosis coefficient and a skewness coefficient equal to zero. In that case, the ERPs of any test (asymptotic or bootstrap) we perform are of the same order.Finally, we provide a new parametric bootstrap using the first four moments of the distribution of the residuals which is as accurate as a non parametric bootstrap which uses these first four moments implicitly. We will introduce it as the parametric bootstrap considering higher moments (CHM), and thus, we will speak about the CHM parametric bootstrap
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by HAL in its series Working Papers with number halshs-00289456.
Date of creation: 20 Jun 2008
Date of revision:
Note: View the original document on HAL open archive server: http://halshs.archives-ouvertes.fr/halshs-00289456/en/
Contact details of provider:
Web page: http://hal.archives-ouvertes.fr/
Non parametric bootstrap; Parametric Bootstrap; Cumulants; Skewness; kurtosis.;
You can help add them by filling out this form.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (CCSD).
If references are entirely missing, you can add them using this form.