15,064 research outputs found
Sample variance in the local measurements of the Hubble constant
The current tension between the Hubble constant measured
from local distance indicators and from cosmic microwave background is one of
the most highly debated issues in cosmology, as it possibly indicates new
physics or unknown systematics. In this work, we explore whether this tension
can be alleviated by the sample variance in the local measurements, which use a
small fraction of the Hubble volume. We use a large-volume cosmological
-body simulation to model the local measurements and to quantify the
variance due to local density fluctuations and sample selection. We explicitly
take into account the inhomogeneous spatial distribution of type Ia supernovae.
Despite the faithful modelling of the observations, our results confirm
previous findings that sample variance in the local Hubble constant measurements is small; we find $\sigma(H_0^{\rm loc})=0.31\,{\rm km\
s^{-1}Mpc^{-1}}\sim6\,{\rm km\
s^{-1}Mpc^{-1}}H_0H_0\sim
150 \,\rm Mpc(\delta\simeq -0.8)\Lambda\LambdaH_0$
measurements even after taking into account the inhomogeneous selection of type
Ia supernovae.Comment: 10 pages, 6 figures, 1 table; main result in Figure 3; replaced to
match published versio
Component selection and smoothing in multivariate nonparametric regression
We propose a new method for model selection and model fitting in multivariate
nonparametric regression models, in the framework of smoothing spline ANOVA.
The ``COSSO'' is a method of regularization with the penalty functional being
the sum of component norms, instead of the squared norm employed in the
traditional smoothing spline method. The COSSO provides a unified framework for
several recent proposals for model selection in linear models and smoothing
spline ANOVA models. Theoretical properties, such as the existence and the rate
of convergence of the COSSO estimator, are studied. In the special case of a
tensor product design with periodic functions, a detailed analysis reveals that
the COSSO does model selection by applying a novel soft thresholding type
operation to the function components. We give an equivalent formulation of the
COSSO estimator which leads naturally to an iterative algorithm. We compare the
COSSO with MARS, a popular method that builds functional ANOVA models, in
simulations and real examples. The COSSO method can be extended to
classification problems and we compare its performance with those of a number
of machine learning algorithms on real datasets. The COSSO gives very
competitive performance in these studies.Comment: Published at http://dx.doi.org/10.1214/009053606000000722 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
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