A family of estimators for multivariate kurtosis in a nonnormal linear regression model
In this paper, we propose a new estimator for a kurtosis in a multivariate nonnormal linear regression model. Usually, an estimator is constructed from an arithmetic mean of the second power of the squared sample Mahalanobis distances between observations and their estimated values. The estimator gives an underestimation and has a large bias, even if the sample size is not small. We replace this squared distance with a transformed squared norm of the Studentized residual using a monotonic increasing function. Our proposed estimator is defined by an arithmetic mean of the second power of these squared transformed squared norms with a correction term and a tuning parameter. The correction term adjusts our estimator to an unbiased estimator under normality, and the tuning parameter controls the sizes of the squared norms of the residuals. The family of our estimators includes estimators based on ordinary least squares and predicted residuals. We verify that the bias of our new estimator is smaller than usual by constructing numerical experiments.
If 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.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Volume (Year): 98 (2007)
Issue (Month): 1 (January)
|Contact details of provider:|| Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description|
|Order Information:|| Postal: http://www.elsevier.com/wps/find/supportfaq.cws_home/regional|
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Fujikoshi, Yasunori, 2000. "Transformations with Improved Chi-Squared Approximations," Journal of Multivariate Analysis, Elsevier, vol. 72(2), pages 249-263, February.
- Klar, Bernhard, 2002. "A Treatment of Multivariate Skewness, Kurtosis, and Related Statistics," Journal of Multivariate Analysis, Elsevier, vol. 83(1), pages 141-165, October.
- Yanagihara, Hirokazu, 2003. "Asymptotic expansion of the null distribution of test statistic for linear hypothesis in nonnormal linear model," Journal of Multivariate Analysis, Elsevier, vol. 84(2), pages 222-246, February.
- Kano, Yutaka, 1992. "Robust statistics for test-of-independence and related structural models," Statistics & Probability Letters, Elsevier, vol. 15(1), pages 21-26, September.
- Yasunori Fujikoshi & Takafumi Noguchi & Megu Ohtaki & Hirokazu Yanagihara, 2003. "Corrected versions of cross-validation criteria for selecting multivariate regression and growth curve models," Annals of the Institute of Statistical Mathematics, Springer, vol. 55(3), pages 537-553, September.
When requesting a correction, please mention this item's handle: RePEc:eee:jmvana:v:98:y:2007:i:1:p:1-29. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei)
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.