The Effect of Sample Design on Principal Component Analysis Export

@article{citeulike:1443098, abstract = {Most sample surveys are multivariate and many lend themselves to multivariate methods of analysis. The most usual mode of such analysis is a standard statistical package, such as BMDP or SPSS, in which the multivariate analyses are based on the underlying assumption that the data are generated as independent observations from a common probability distribution. This assumption ignores the sample selection procedure involved in the survey, which leads to the following basic questions. What effects can the sample design have on methods of multivariate analysis? How should such effects be taken into account? This article considers the case of principal component analysis and, in particular, the point estimation of the eigenvalues and eigenvectors of a covariance matrix. It is assumed that the selection of the sample depends on the population values of auxiliary variables as, for example, in stratified sampling. The conventional estimators, based on the assumption of simple random sampling, are compared with alternative probability-weighted and maximum likelihood estimators. Under a multivariate normal model, simple expressions are presented for the approximate model bias of the different estimators. The validity of these results is assessed in a simulation study involving a disproportionate stratified design.}, author = {Skinner, C. J. and Holmes, D. J. and Smith, T. M. F.}, citeulike-article-id = {1443098}, citeulike-linkout-0 = {http://www.jstor.org/stable/2289011}, journal = {Journal of the American Statistical Association}, keywords = {pca, sampling, survey}, number = {395}, pages = {789--798}, posted-at = {2007-07-08 19:45:48}, priority = {2}, title = {The Effect of Sample Design on Principal Component Analysis}, url = {http://www.jstor.org/stable/2289011}, volume = {81}, year = {1986} }

TY - JOUR ID - citeulike:1443098 L3 - citeulike-article-id:1443098 N2 - Most sample surveys are multivariate and many lend themselves to multivariate methods of analysis. The most usual mode of such analysis is a standard statistical package, such as BMDP or SPSS, in which the multivariate analyses are based on the underlying assumption that the data are generated as independent observations from a common probability distribution. This assumption ignores the sample selection procedure involved in the survey, which leads to the following basic questions. What effects can the sample design have on methods of multivariate analysis? How should such effects be taken into account? This article considers the case of principal component analysis and, in particular, the point estimation of the eigenvalues and eigenvectors of a covariance matrix. It is assumed that the selection of the sample depends on the population values of auxiliary variables as, for example, in stratified sampling. The conventional estimators, based on the assumption of simple random sampling, are compared with alternative probability-weighted and maximum likelihood estimators. Under a multivariate normal model, simple expressions are presented for the approximate model bias of the different estimators. The validity of these results is assessed in a simulation study involving a disproportionate stratified design. IS - 395 JF - Journal of the American Statistical Association EP - 798 TI - The Effect of Sample Design on Principal Component Analysis VL - 81 SP - 789 KW - pca KW - sampling KW - survey AU - Skinner, CJ AU - Holmes, DJ AU - Smith, TMF PY - 1986/// UR - http://www.jstor.org/stable/2289011 ER -