TY - JOUR

T1 - Nonparametric inference in multivariate mixtures

AU - Hall, Peter

AU - Neeman, Amnon

AU - Pakyari, Reza

AU - Elmore, Ryan

PY - 2005/9

Y1 - 2005/9

N2 - We consider mixture models in which the components of data vectors from any given subpopulation are statistically independent, or independent in blocks. We argue that if, under this condition of independence, we take a nonparametric view of the problem and allow the number of subpopulations to be quite general, the distributions and mixing proportions can often be estimated root-n consistently. Indeed, we show that, if the data are k-variate and there are p subpopulations, then for each p ≥ 2 there is a minimal value of k, k p say, such that the mixture problem is always nonparametrically identifiable, and all distributions and mixture proportions are nonparametrically identifiable when k≥kp. We treat the case p = 2 in detail, and there we show how to construct explicit distribution, density and mixture-proportion estimators, converging at conventional rates. Other values of p can be addressed using a similar approach, although the methodology becomes rapidly more complex as p increases.

AB - We consider mixture models in which the components of data vectors from any given subpopulation are statistically independent, or independent in blocks. We argue that if, under this condition of independence, we take a nonparametric view of the problem and allow the number of subpopulations to be quite general, the distributions and mixing proportions can often be estimated root-n consistently. Indeed, we show that, if the data are k-variate and there are p subpopulations, then for each p ≥ 2 there is a minimal value of k, k p say, such that the mixture problem is always nonparametrically identifiable, and all distributions and mixture proportions are nonparametrically identifiable when k≥kp. We treat the case p = 2 in detail, and there we show how to construct explicit distribution, density and mixture-proportion estimators, converging at conventional rates. Other values of p can be addressed using a similar approach, although the methodology becomes rapidly more complex as p increases.

KW - Bandwidth

KW - Curve estimation

KW - Independent marginals

KW - Kernel methods

KW - Nonparametric density estimation

UR - http://www.scopus.com/inward/record.url?scp=24144451098&partnerID=8YFLogxK

U2 - 10.1093/biomet/92.3.667

DO - 10.1093/biomet/92.3.667

M3 - Article

SN - 0006-3444

VL - 92

SP - 667

EP - 678

JO - Biometrika

JF - Biometrika

IS - 3

ER -