8,168 research outputs found
Penalized Clustering of Large Scale Functional Data with Multiple Covariates
In this article, we propose a penalized clustering method for large scale
data with multiple covariates through a functional data approach. In the
proposed method, responses and covariates are linked together through
nonparametric multivariate functions (fixed effects), which have great
flexibility in modeling a variety of function features, such as jump points,
branching, and periodicity. Functional ANOVA is employed to further decompose
multivariate functions in a reproducing kernel Hilbert space and provide
associated notions of main effect and interaction. Parsimonious random effects
are used to capture various correlation structures. The mixed-effect models are
nested under a general mixture model, in which the heterogeneity of functional
data is characterized. We propose a penalized Henderson's likelihood approach
for model-fitting and design a rejection-controlled EM algorithm for the
estimation. Our method selects smoothing parameters through generalized
cross-validation. Furthermore, the Bayesian confidence intervals are used to
measure the clustering uncertainty. Simulation studies and real-data examples
are presented to investigate the empirical performance of the proposed method.
Open-source code is available in the R package MFDA
Modelling the number counts of early-type galaxies by pure luminosity evolution
In this paper, we explore the plausible luminosity evolution of early-type
galaxies in different cosmological models by constructing a set of pure
luminosity evolution (PLE) models via the choices of the star formation rate
(SFR) parameters and formation redshift of galaxies, with the
observational constraints derived from the Hubble Space Telescope (HST)
morphological number counts for elliptical and S0 galaxies of the Medium Deep
Survey (MDS) and the Hubble Deep Field (HDF). We find that the number counts of
early-type galaxies can be explained by the pure luminosity evolution models,
without invoking exotic scenarios such as merging or introducing an additional
population. But the evolution should be nearly passive, with a high
assumed. The conclusion is valid in all of the three cosmological models we
adopted in this paper. We also present the redshift distributions for three
bins of observed magnitudes in F814w pass-band, to show at which redshift are
the objects that dominate the counts at a given magnitude. The predictions of
the redshift distribution of are also presented for comparison
with future data.Comment: Plain tex, 15pages, 9 eps figures, plus an extra figure fig2c.eps,
with the tex-macro mn.tex. MNRAS, accepte
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