40 research outputs found
Lambert W random variables - a new family of generalized skewed distributions with applications to risk estimation
Originating from a system theory and an input/output point of view, I
introduce a new class of generalized distributions. A parametric nonlinear
transformation converts a random variable into a so-called Lambert
random variable , which allows a very flexible approach to model skewed
data. Its shape depends on the shape of and a skewness parameter .
In particular, for symmetric and nonzero the output is skewed.
Its distribution and density function are particular variants of their input
counterparts. Maximum likelihood and method of moments estimators are
presented, and simulations show that in the symmetric case additional
estimation of does not affect the quality of other parameter
estimates. Applications in finance and biomedicine show the relevance of this
class of distributions, which is particularly useful for slightly skewed data.
A practical by-result of the Lambert framework: data can be "unskewed." The
package http://cran.r-project.org/web/packages/LambertWLambertW developed
by the author is publicly available (http://cran.r-project.orgCRAN).Comment: Published in at http://dx.doi.org/10.1214/11-AOAS457 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Forecastable Component Analysis (ForeCA)
I introduce Forecastable Component Analysis (ForeCA), a novel dimension
reduction technique for temporally dependent signals. Based on a new
forecastability measure, ForeCA finds an optimal transformation to separate a
multivariate time series into a forecastable and an orthogonal white noise
space. I present a converging algorithm with a fast eigenvector solution.
Applications to financial and macro-economic time series show that ForeCA can
successfully discover informative structure, which can be used for forecasting
as well as classification. The R package ForeCA
(http://cran.r-project.org/web/packages/ForeCA/index.html) accompanies this
work and is publicly available on CRAN.Comment: 10 pages, 4 figures; ICML 201
Mixed LICORS: A Nonparametric Algorithm for Predictive State Reconstruction
We introduce 'mixed LICORS', an algorithm for learning nonlinear,
high-dimensional dynamics from spatio-temporal data, suitable for both
prediction and simulation. Mixed LICORS extends the recent LICORS algorithm
(Goerg and Shalizi, 2012) from hard clustering of predictive distributions to a
non-parametric, EM-like soft clustering. This retains the asymptotic predictive
optimality of LICORS, but, as we show in simulations, greatly improves
out-of-sample forecasts with limited data. The new method is implemented in the
publicly-available R package "LICORS"
(http://cran.r-project.org/web/packages/LICORS/).Comment: 11 pages; AISTATS 201
Mixed LICORS: A Nonparametric Algorithm for Predictive State Reconstruction
Abstract We introduce mixed LICORS, an algorithm for learning nonlinear, high-dimensional dynamics from spatio-temporal data, suitable for both prediction and simulation. Mixed LICORS extends the recent LICORS algorithm (Goerg and Shalizi, 2012) from hard clustering of predictive distributions to a non-parametric, EM-like soft clustering. This retains the asymptotic predictive optimality of LICORS, but, as we show in simulations, greatly improves out-of-sample forecasts with limited data. The new method is implemented in the publicly-available R package LICORS