Details
| Originalsprache | Englisch |
|---|---|
| Seiten (von - bis) | 37-70 |
| Seitenumfang | 34 |
| Fachzeitschrift | Electronic journal of statistics |
| Jahrgang | 15 |
| Ausgabenummer | 1 |
| Publikationsstatus | Veröffentlicht - 2021 |
Abstract
We investigate existence and properties of discrete mixture representations Pθ = ∑i∈Ewθ(i) Qi for a given family Pθ, θ ∈Θ, of probability measures. The noncentral chi-squared distributions provide a classi-cal example. We obtain existence results and results about geometric and statistical aspects of the problem, the latter including loss of Fisher in-formation, Rao-Blackwellization, asymptotic efficiency and nonparametric maximum likelihood estimation of the mixing probabilities.
ASJC Scopus Sachgebiete
- Mathematik (insg.)
- Statistik und Wahrscheinlichkeit
- Entscheidungswissenschaften (insg.)
- Statistik, Wahrscheinlichkeit und Ungewissheit
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in: Electronic journal of statistics, Jahrgang 15, Nr. 1, 2021, S. 37-70.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review
}
TY - JOUR
T1 - Discrete mixture representations of parametric distribution families
T2 - Geometry and statistics
AU - Baringhaus, Ludwig
AU - Grübel, Rudolf
N1 - Publisher Copyright: © 2021, Institute of Mathematical Statistics. All rights reserved.
PY - 2021
Y1 - 2021
N2 - We investigate existence and properties of discrete mixture representations Pθ = ∑i∈Ewθ(i) Qi for a given family Pθ, θ ∈Θ, of probability measures. The noncentral chi-squared distributions provide a classi-cal example. We obtain existence results and results about geometric and statistical aspects of the problem, the latter including loss of Fisher in-formation, Rao-Blackwellization, asymptotic efficiency and nonparametric maximum likelihood estimation of the mixing probabilities.
AB - We investigate existence and properties of discrete mixture representations Pθ = ∑i∈Ewθ(i) Qi for a given family Pθ, θ ∈Θ, of probability measures. The noncentral chi-squared distributions provide a classi-cal example. We obtain existence results and results about geometric and statistical aspects of the problem, the latter including loss of Fisher in-formation, Rao-Blackwellization, asymptotic efficiency and nonparametric maximum likelihood estimation of the mixing probabilities.
KW - Asymptotic efficiency
KW - Barycenter convexity
KW - Chi-squared distribution families
KW - EM algorithm
KW - Estimation of mixing probabilities
KW - Fisher information
KW - Mixture distribution
UR - http://www.scopus.com/inward/record.url?scp=85099845301&partnerID=8YFLogxK
U2 - 10.48550/arXiv.2206.11094
DO - 10.48550/arXiv.2206.11094
M3 - Article
AN - SCOPUS:85099845301
VL - 15
SP - 37
EP - 70
JO - Electronic journal of statistics
JF - Electronic journal of statistics
SN - 1935-7524
IS - 1
ER -