A Problem of Dimensionality in Normal Mixture Analysis

Marco Bee and Bernard Flury

Scandinavian Journal of Statistics, 2002, vol. 29, issue 3, 485-500

Abstract: Suppose the p‐variate random vector W, partitioned into q variables W1 and p‐q variables W2, follows a multivariate normal mixture distribution. If the investigator is mainly interested in estimation of the parameters of the distribution of W1, there are two possibilities: (1) use only the data on W1 for estimation, and (2) estimate the parameters of the p‐variate mixture distribution, and then extract the estimates of the marginal distribution of W1. In this article we study the choice between these two possibilities mainly for the case of two mixture components with identical covariance matrices. We find the asymptotic distribution of the linear discriminant function coefficients using the work of Efron (1975) and O'Neill (1978), and give a Wald–test for redundancy of W2. A simulation study gives further insights into conditions under which W2 should be used in the analysis: in summary, the inclusion of W2 seems justified if Δ 2.1, the Mahalanobis distance between the two component distributions based on the conditional distribution of W2 given W1, is at least 2.

Date: 2002
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1111/1467-9469.00302

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:bla:scjsta:v:29:y:2002:i:3:p:485-500

Ordering information: This journal article can be ordered from
http://www.blackwell ... bs.asp?ref=0303-6898

Access Statistics for this article

Scandinavian Journal of Statistics is currently edited by ÿrnulf Borgan and Bo Lindqvist

More articles in Scandinavian Journal of Statistics from Danish Society for Theoretical Statistics, Finnish Statistical Society, Norwegian Statistical Association, Swedish Statistical Association
Bibliographic data for series maintained by Wiley Content Delivery ().