Almost nonparametric inference for repeated measures in mixture models

By Thomas P. Hettmansperger, H. Thomas. 2000

65 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/fc91e8b3def1bee424972336fd6aeb6ad676bdc9

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In Artificial Intelligence

In Statistics and Probability

Citations in the corpus

Maximum smoothed likelihood for multivariate mixtures (2011, methodology): “The second part of the M-step (17) becomes • M-step, part 2: For each component j and block ℓ ∈ {1, . . . , B}, let f t+1jℓ (u) = ∑r k=1 ∑n i=1w t ijI{bk=ℓ}Kh (u− xik) ∑r k=1 ∑n i=1w t ijI{bk=ℓ} = 1 nhλt+1j Cℓ r ∑ k=1 n ∑ i=1 wtijI{bk=ℓ}K ( u− xik h ) , (19) where Cℓ = ∑r k=1 I{bk=ℓ} is the number…”
Semi-Parametric Estimation for Conditional Independence Multivariate Finite Mixture Models (2015, methodology): “The Water-level dataset To illustrate the adaptive block- and component-wise bandwidth approach, we consider a benchmark dataset previously analyzed by Hettmansperger and Thomas [22] and Elmore et al.”
Inference for mixtures of symmetric distributions (2007, background): “ component distributions are assumed to come from a known parametric family, relatively little work has been done in the case where minimal assumptions are made regarding G. Hettmansperger and Thomas [7] report promising results when the component distributions are multivariate, by reducing the mode”
Nonparametric Identification of Multivariate Mixtures (2010, methodology): “As emphasized in Hettmansperger and Thomas (2000), there is often little theoretical guidance for selecting the number of components and/or the form of the component distributions despite their key role in the specification of mixtures.”
mixtools: An R Package for Analyzing Mixture Models (2009, background): “One such set of conditions is as follows: Hettmansperger and Thomas (2000); Cruz-Medina, Hettmansperger, and Thomas (2004); and Elmore, Hettmansperger, and Thomas (2004) treat the case in which φ j ( x ) equals the product · · · Thus, conditional on knowing that X comes from the j th mixture…”
Non‐parametric identification and estimation of the number of components in multivariate mixtures (2014, methodology): “Hettmansperger and Thomas (2000) applied various tests of the number of components to the data transformed to a binomial mixture: Lindsay’s (1995) gradient function method suggests M =4, the Hellinger and the Pearson penalized distances suggest M = 2 and the bootstrapped likelihood ratio test…”
Non‐parametric estimation of finite mixtures from repeated measurements (2016, methodology): “Popular applications include modelling unobserved heterogeneity in structural behavioural models, learning about individual behaviour from grouped data and dealing with corrupted data.”
Identifiability of parameters in latent structure models with many observed variables (2008, methodology): “Nonparametric mixture models have received much attention recently [4, 25, 26].”