14,601 research outputs found
Generalized Additive Modeling For Multivariate Distributions
In this thesis, we develop tools to study the influence of predictors on multivariate distributions. We tackle the issue of conditional dependence modeling using generalized additive models, a natural extension of linear and generalized linear models allowing for smooth functions of the covariates. Compared to existing methods, the framework that we develop has two main advantages. First, it is completely flexible, in the sense that the dependence structure can vary with an arbitrary set of covariates in a parametric, nonparametric or semiparametric way. Second, it is both quick and numerically stable, which means that it is suitable for exploratory data analysis and stepwise model building. Starting from the bivariate case, we extend our framework to pair-copula constructions, and open new possibilities for further applied and methodological work. Our regression-like theory of the dependence, being built on conditional copulas and generalized additive models, is at the same time theoretically sound and practically useful
Brownian distance covariance
Distance correlation is a new class of multivariate dependence coefficients
applicable to random vectors of arbitrary and not necessarily equal dimension.
Distance covariance and distance correlation are analogous to product-moment
covariance and correlation, but generalize and extend these classical bivariate
measures of dependence. Distance correlation characterizes independence: it is
zero if and only if the random vectors are independent. The notion of
covariance with respect to a stochastic process is introduced, and it is shown
that population distance covariance coincides with the covariance with respect
to Brownian motion; thus, both can be called Brownian distance covariance. In
the bivariate case, Brownian covariance is the natural extension of
product-moment covariance, as we obtain Pearson product-moment covariance by
replacing the Brownian motion in the definition with identity. The
corresponding statistic has an elegantly simple computing formula. Advantages
of applying Brownian covariance and correlation vs the classical Pearson
covariance and correlation are discussed and illustrated.Comment: This paper discussed in: [arXiv:0912.3295], [arXiv:1010.0822],
[arXiv:1010.0825], [arXiv:1010.0828], [arXiv:1010.0836], [arXiv:1010.0838],
[arXiv:1010.0839]. Rejoinder at [arXiv:1010.0844]. Published in at
http://dx.doi.org/10.1214/09-AOAS312 the Annals of Applied Statistics
(http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics
(http://www.imstat.org
A two-step approach to model precipitation extremes in California based on max-stable and marginal point processes
In modeling spatial extremes, the dependence structure is classically
inferred by assuming that block maxima derive from max-stable processes.
Weather stations provide daily records rather than just block maxima. The point
process approach for univariate extreme value analysis, which uses more
historical data and is preferred by some practitioners, does not adapt easily
to the spatial setting. We propose a two-step approach with a composite
likelihood that utilizes site-wise daily records in addition to block maxima.
The procedure separates the estimation of marginal parameters and dependence
parameters into two steps. The first step estimates the marginal parameters
with an independence likelihood from the point process approach using daily
records. Given the marginal parameter estimates, the second step estimates the
dependence parameters with a pairwise likelihood using block maxima. In a
simulation study, the two-step approach was found to be more efficient than the
pairwise likelihood approach using only block maxima. The method was applied to
study the effect of El Ni\~{n}o-Southern Oscillation on extreme precipitation
in California with maximum daily winter precipitation from 35 sites over 55
years. Using site-specific generalized extreme value models, the two-step
approach led to more sites detected with the El Ni\~{n}o effect, narrower
confidence intervals for return levels and tighter confidence regions for risk
measures of jointly defined events.Comment: Published at http://dx.doi.org/10.1214/14-AOAS804 in the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
SPACE-TIME LAGS: SPECIFICATION STRATEGY IN SPATIAL REGRESSION MODELS
he purpose of this article is to analyse the dynamic trend of spatial dependence, which is not only contemporary but time-lagged in many socio-economic phenomena. Firstly, we show some of the commonly used exploratory spatial data analysis (ESDA) techniques and we propose other new ones, the exploratory space-time data analysis (ESTDA) that evaluates the instantaneity of spatial dependence. We also propose the space-time correlogram as an instrument for a better specification of spatial lag models, which should include both kind of spatial dependence. Some applications with economic data for Spanish provinces shed some light upon these issues.Spatial dependence, spatial diffusion, ESDA, correlogram, Spanish provinces
Nonlinear cross-spectrum analysis via the local Gaussian correlation
Spectrum analysis can detect frequency related structures in a time series
, but may in general be an inadequate tool if
asymmetries or other nonlinear phenomena are present. This limitation is a
consequence of the way the spectrum is based on the second order moments (auto
and cross-covariances), and alternative approaches to spectrum analysis have
thus been investigated based on other measures of dependence. One such approach
was developed for univariate time series in Jordanger and Tj{\o}stheim (2017),
where it was seen that a local Gaussian auto-spectrum , based on
the local Gaussian autocorrelations from Tj{\o}stheim and
Hufthammer (2013), could detect local structures in time series that looked
like white noise when investigated by the ordinary auto-spectrum .
The local Gaussian approach in this paper is extended to a local Gaussian
cross-spectrum for multivariate time series. The local
cross-spectrum has the desirable property that it coincides
with the ordinary cross-spectrum for Gaussian time series,
which implies that can be used to detect non-Gaussian traits
in the time series under investigation. In particular: If the ordinary spectrum
is flat, then peaks and troughs of the local Gaussian spectrum can indicate
nonlinear traits, which potentially might discover local periodic phenomena
that goes undetected in an ordinary spectral analysis.Comment: 41 pages, 12 figure
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