On improved estimation of normal precision matrix and discriminant coefficients
The problem of estimating the precision matrix of a multivariate normal distribution model is considered with respect to a quadratic loss function. A number of covariance estimators originally intended for a variety of loss functions are adapted so as to obtain alternative estimators of the precision matrix. It is shown that the alternative estimators have analytically smaller risks than the unbiased estimator of the precision matrix. Through numerical studies of risk values, it is shown that the new estimators have substantial reduction in risk. In addition, we consider the problem of the estimation of discriminant coefficients, which arises in linear discriminant analysis when Fisher's linear discriminant function is viewed as the posterior log-odds under the assumption that two classes differ in mean but have a common covariance matrix. The above method is also adapted for this problem in order to obtain improved estimators of the discriminant coefficients under the quadratic loss function. Furthermore, a numerical study is undertaken to compare the properties of a collection of alternatives to the "unbiased" estimator of the discriminant coefficients.
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): 97 (2006)
Issue (Month): 7 (August)
|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.:
- Haff, L. R., 1979. "An identity for the Wishart distribution with applications," Journal of Multivariate Analysis, Elsevier, vol. 9(4), pages 531-544, December.
- Dey D. K. & Ghosh M. & Srinivasan C., 1990. "A New Class Of Improved Estimators Of A Multinormal Precision Matrix," Statistics & Risk Modeling, De Gruyter, vol. 8(2), pages 141-152, February.
- Xian Zhou & Xiaoqian Sun & Jinglong Wang, 2001. "Estimation of the Multivariate Normal Precision Matrix under the Entropy Loss," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 53(4), pages 760-768, December.
- Haff, L. R., 1977. "Minimax estimators for a multinormal precision matrix," Journal of Multivariate Analysis, Elsevier, vol. 7(3), pages 374-385, September.
- Dey, Dipak K. & Srinivasan, C., 1991. "On estimation of discriminant coefficients," Statistics & Probability Letters, Elsevier, vol. 11(3), pages 189-193, March.
- Dey, Dipak K., 1987. "Improved estimation of a multinormal precision matrix," Statistics & Probability Letters, Elsevier, vol. 6(2), pages 125-128, November.
- Perron, F., 1992. "Minimax estimators of a covariance matrix," Journal of Multivariate Analysis, Elsevier, vol. 43(1), pages 16-28, October.
When requesting a correction, please mention this item's handle: RePEc:eee:jmvana:v:97:y:2006:i:7:p:1477-1500. 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: (Dana Niculescu)
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.