6,115 research outputs found
On nonparametric estimation of a mixing density via the predictive recursion algorithm
Nonparametric estimation of a mixing density based on observations from the
corresponding mixture is a challenging statistical problem. This paper surveys
the literature on a fast, recursive estimator based on the predictive recursion
algorithm. After introducing the algorithm and giving a few examples, I
summarize the available asymptotic convergence theory, describe an important
semiparametric extension, and highlight two interesting applications. I
conclude with a discussion of several recent developments in this area and some
open problems.Comment: 22 pages, 5 figures. Comments welcome at
https://www.researchers.one/article/2018-12-
Dirichlet process mixtures under affine transformations of the data
Location-scale Dirichlet process mixtures of Gaussians (DPM-G) have proved
extremely useful in dealing with density estimation and clustering problems in
a wide range of domains. Motivated by an astronomical application, in this work
we address the robustness of DPM-G models to affine transformations of the
data, a natural requirement for any sensible statistical method for density
estimation and clustering. First, we devise a coherent prior specification of
the model which makes posterior inference invariant with respect to affine
transformations of the data. Second, we formalise the notion of asymptotic
robustness under data transformation and show that mild assumptions on the true
data generating process are sufficient to ensure that DPM-G models feature such
a property. Our investigation is supported by an extensive simulation study and
illustrated by the analysis of an astronomical dataset consisting of physical
measurements of stars in the field of the globular cluster NGC 2419.Comment: 36 pages, 7 Figure
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