Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Identifiability and optimal rates of convergence for parameters of
  multiple types in finite mixtures   This paper studies identifiability and convergence behaviors for parameters
of multiple types in finite mixtures, and the effects of model fitting with
extra mixing components. First, we present a general theory for strong
identifiability, which extends from the previous work of Nguyen [2013] and Chen
[1995] to address a broad range of mixture models and to handle matrix-variate
parameters. These models are shown to share the same Wasserstein distance based
optimal rates of convergence for the space of mixing distributions ---
$n^{-1/2}$ under $W_1$ for the exact-fitted and $n^{-1/4}$ under $W_2$ for the
over-fitted setting, where $n$ is the sample size. This theory, however, is not
applicable to several important model classes, including location-scale
multivariate Gaussian mixtures, shape-scale Gamma mixtures and
location-scale-shape skew-normal mixtures. The second part of this work is
devoted to demonstrating that for these "weakly identifiable" classes,
algebraic structures of the density family play a fundamental role in
determining convergence rates of the model parameters, which display a very
rich spectrum of behaviors. For instance, the optimal rate of parameter
estimation in an over-fitted location-covariance Gaussian mixture is precisely
determined by the order of a solvable system of polynomial equations --- these
rates deteriorate rapidly as more extra components are added to the model. The
established rates for a variety of settings are illustrated by a simulation
study.

3
The categories of this paper are: physics
4
The categories of this paper are: cond-mat
12
The categories of this paper are: nucl-th
18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph
27
The categories of this paper are: comp-gas
5
The categories of this paper are: gr-qc
29
The categories of this paper are: funct-an
33
The categories of this paper are: plasm-ph
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The categories of this paper are: q-fin
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The categories of this paper are: adap-org
8
The categories of this paper are: hep-ex
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The categories of this paper are: nlin
32
The categories of this paper are: atom-ph
0
The categories of this paper are: hep-ph
30
The categories of this paper are: q-alg