977 research outputs found
Saddlepoint approximations for noncentral quadratic forms
Many estimators and tests are of the form of a ratio of quadratic forms in normal variables. Excepting a few very special cases little is known about the density or distribution of these ratios, particularly if we allow for noncentrality in the quadratic forms. This paper assumes this generality and derives saddlepoint approximations for this class of statistics. We first derive and prove the existence of an exact inversion based on the joint characteristic function. Then the saddlepoint algorithm is applied and the leading term found, and analytic justification of the asymptotic nature of the approximation is given. As an illustration we consider the calculation of sizes and powers of F-tests, where a new exact result is found
Long-memory process and aggregation of AR(1) stochastic processes: A new characterization
Contemporaneous aggregation of individual AR(1) random processes might lead
to different properties of the limit aggregated time series, in particular,
long memory (Granger, 1980). We provide a new characterization of the series of
autoregressive coefficients, which is defined from the Wold representation of
the limit of the aggregate stochastic process, in the presence of long-memory
features. Especially the infinite autoregressive stochastic process defined by
the almost sure representation of the aggregate process has a unit root in the
presence of the long-memory property. Finally we discuss some examples using
some well-known probability density functions of the autoregressive random
parameter in the aggregation literature. JEL Classification Code: C2, C13
Galaxy-galaxy Lensing: Dissipationless Simulations Versus the Halo Model
Galaxy-galaxy lensing is a powerful probe of the relation between galaxies
and dark matter halos, but its theoretical interpretation requires a careful
modeling of various contributions, such as the contribution from central and
satellite galaxies. For this purpose, a phenomenological approach based on the
halo model has been developed, allowing for fast exploration of the parameter
space of models. In this paper, we investigate the ability of the halo model to
extract information from the g-g weak lensing signal by comparing it to
high-resolution dissipationless simulations that resolve subhalos. We find that
the halo model reliably determines parameters such as the host halo mass of
central galaxies, the fraction of galaxies that are satellites, and their
radial distribution inside larger halos. If there is a significant scatter
present in the central galaxy host halo mass distribution, then the mean and
median mass of that distribution can differ significantly from one another, and
the halo model mass determination lies between the two. This result suggests
that when analyzing the data, galaxy subsamples with a narrow central galaxy
halo mass distribution, such as those based on stellar mass, should be chosen
for a simpler interpretation of the results.Comment: 13 pages, 6 figures; minor changes made, matches MNRAS accepted
versio
On Some Unifications Arising from the MIMO Rician Shadowed Model
This paper shows that the proposed Rician shadowed model for multi-antenna communications allows for the unification of a wide set of models, both for multiple-input multiple-output (MIMO) and single- input single-output (SISO) communications. The MIMO Rayleigh and MIMO Rician can be deduced from the MIMO Rician shadowed, and so their SISO counterparts. Other more general SISO models, besides the Rician shadowed, are included in the model, such as the κ-μ, and its recent generalization, the κ-μ shadowed model. Moreover, the SISO η-μ and Nakagami-q models are also included in the MIMO Rician shadowed model. The literature already presents the probability density function (pdf) of the Rician shadowed Gram channel matrix in terms of the well-known gamma- Wishart distribution. We here derive its moment generating function in a tractable form. Closed- form expressions for the cumulative distribution function and the pdf of the maximum eigenvalue are also carried out.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech
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
Maximum Likelihood Estimation of Latent Affine Processes
This article develops a direct filtration-based maximum likelihood methodology for estimating the parameters and realizations of latent affine processes. The equivalent of Bayes' rule is derived for recursively updating the joint characteristic function of latent variables and the data conditional upon past data. Likelihood functions can consequently be evaluated directly by Fourier inversion. An application to daily stock returns over 1953-96 reveals substantial divergences from EMM-based estimates: in particular, more substantial and time-varying jump risk.
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