NONPARAMETRIC ESTIMATION OF COMPONENT DISTRIBUTIONS IN A MULTIVARIATE MIXTURE

By Peter Hall, Xiao-Hua Zhou. 2003

266 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Statistics and Probability

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Citations in the corpus

Identifying Finite Mixtures of Nonparametric Product Distributions and Causal Inference of Confounders (2013, background): “Hall & Zhou (2003) proved that when m = 2, identiﬁability of parameters always holds in d ≥ 3 dimensions.”
Identifiability of parameters in latent structure models with many observed variables (2008, background): “Nonparametric mixture models have received much attention recently [4, 25, 26].”
SEMIPARAMETRIC ESTIMATION OF A TWO-COMPONENT MIXTURE MODEL (2006, background): “The Annals of Statistics 2006, Vol. 34, No. 3, 1204–1232 DOI: 10.1214/009053606000000353 © Institute of Mathematical Statistics, 2006 SEMIPARAMETRIC ESTIMATION OF A TWO-COMPONENT MIXTURE MODEL”
Using mixtures in econometric models: a brief review and some new results (2016, methodology): “Further, Allman et al. (2009) show that Hall and Zhou (2003) can be viewed as a special case of a more general model in which identification comes from applying an algebraic result on three-way arrays by Kruskal (1977).”
On strong identifiability and convergence rates of parameter estimation in finite mixtures (2016, background): “Keywords and phrases: mixture models, strong identifiability, Wasserstein distances, minimax bounds, maximum likelihood estimation.”
Inference for mixtures of symmetric distributions (2007, unknown): “utpoints. In their case, the data consist of vectors of repeated measures, assumed to be independent and identically distributed, conditional on the component from which they are drawn. Hall and Zhou [6] discuss a related situation in which the repeated measures are independent but not identically d”
Nonparametric Identification of Finite Mixture Models of Dynamic Discrete Choices (2009, methodology): “The finite mixture models studied by Hall and Zhou (2003) have no covariates as discussed in the introduction.”
Inference in finite state space non parametric Hidden Markov Models and applications (2015, methodology): “Identiﬁabil-ity of non parametric mixtures of two multivariate distributions of vectors of independent random variables has been investigated in a seminal paper by Hall and Zhou (2003) and further extended by Allman et al. (2009).”
Probabilistic forecasting from ensemble prediction systems: Improving upon the best‐member method by using a different weight and dressing kernel for each member (2006, methodology): “…that univariate mixture models of this type are known to be non-identifiable from a nonparametric viewpoint when no training data are available (Hall and Zhou 2003), meaning that we must rely on an arbitrary allocation algorithm, such as the best-member approach, to build a training dataset…”
A Distributional Framework for Matched Employer Employee Data (2019, methodology): “Our approach to identification and estimation of mixture models has a number of precedents in the literature, such as Hall and Zhou (2003), Hu (2008), Henry et al. (2014), Levine et al. (2011), Bonhomme et al. (2014), and Hu and Schennach (2008) and Hu and Shum (2012) for continuous mixtures.”
Econometric Analysis of Games with Multiple Equilibria (2012, methodology): “This is a mixture of independent random variables, and results such as those by Hall & Zhou (2003) can be used to demonstrate that the component distribution ðpk1ðx Þ, pk2ðx ÞÞ jEðx ,u,F Þj k¼1 andmixing probabilities are not point identified by the model if jE(x , u, F )j is strictly greater than…”
Non‐parametric estimation of finite mixtures from repeated measurements (2016, methodology): “These approaches are applicable more generally than are the earlier proposals of Hettmansperger and Thomas (2000) and Elmore, Hettmansperger, and Thomas (2004), and of Hall and Zhou (2003) and Hall, Neeman, Pakyari, and Elmore (2005).”
Maximum smoothed likelihood for multivariate mixtures (2011, background): “Hall and Zhou (2003) established that when m = 2, identifiability of parameters generally follows in r ≥ 3 dimensions but not in fewer than three.”
Nonparametric Identification of Multivariate Mixtures (2010, methodology): “, Fm j (wj) = F (wj) for all j’s), Hettmansperger and Thomas (2000) and Cruz-Medina et al. (2004) transform the data into binomial or multinomial variables and apply the results on the identifiability of binomial and multinomial mixtures of Blischke (1964) and Elmore and Wang (2003).”