80,794 research outputs found
Variance Estimation in a Random Coefficients Model
This papers describes an estimator for a standard state-space model with coefficients generated by a random walk that is statistically superior to the Kalman filter as applied to this particular class of models. Two closely related estimators for the variances are introduced: A maximum likelihood estimator and a moments estimator that builds on the idea that some moments are equalized to their expectations. These estimators perform quite similar in many cases. In some cases, however, the moments estimator is preferable both to the proposed likelihood estimator and the Kalman filter, as implemented in the program package Eviews
High-Dimensional Density Ratio Estimation with Extensions to Approximate Likelihood Computation
The ratio between two probability density functions is an important component
of various tasks, including selection bias correction, novelty detection and
classification. Recently, several estimators of this ratio have been proposed.
Most of these methods fail if the sample space is high-dimensional, and hence
require a dimension reduction step, the result of which can be a significant
loss of information. Here we propose a simple-to-implement, fully nonparametric
density ratio estimator that expands the ratio in terms of the eigenfunctions
of a kernel-based operator; these functions reflect the underlying geometry of
the data (e.g., submanifold structure), often leading to better estimates
without an explicit dimension reduction step. We show how our general framework
can be extended to address another important problem, the estimation of a
likelihood function in situations where that function cannot be
well-approximated by an analytical form. One is often faced with this situation
when performing statistical inference with data from the sciences, due the
complexity of the data and of the processes that generated those data. We
emphasize applications where using existing likelihood-free methods of
inference would be challenging due to the high dimensionality of the sample
space, but where our spectral series method yields a reasonable estimate of the
likelihood function. We provide theoretical guarantees and illustrate the
effectiveness of our proposed method with numerical experiments.Comment: With supplementary materia
Gravitational Wave Burst Source Direction Estimation using Time and Amplitude Information
In this article we study two problems that arise when using timing and
amplitude estimates from a network of interferometers (IFOs) to evaluate the
direction of an incident gravitational wave burst (GWB). First, we discuss an
angular bias in the least squares timing-based approach that becomes
increasingly relevant for moderate to low signal-to-noise ratios. We show how
estimates of the arrival time uncertainties in each detector can be used to
correct this bias. We also introduce a stand alone parameter estimation
algorithm that can improve the arrival time estimation and provide
root-sum-squared strain amplitude (hrss) values for each site. In the second
part of the paper we discuss how to resolve the directional ambiguity that
arises from observations in three non co-located interferometers between the
true source location and its mirror image across the plane containing the
detectors. We introduce a new, exact relationship among the hrss values at the
three sites that, for sufficiently large signal amplitudes, determines the true
source direction regardless of whether or not the signal is linearly polarized.
Both the algorithm estimating arrival times, arrival time uncertainties, and
hrss values and the directional follow-up can be applied to any set of
gravitational wave candidates observed in a network of three non co-located
interferometers. As a case study we test the methods on simulated waveforms
embedded in simulations of the noise of the LIGO and Virgo detectors at design
sensitivity.Comment: 10 pages, 14 figures, submitted to PR
ppmlhdfe: Fast Poisson Estimation with High-Dimensional Fixed Effects
In this paper we present ppmlhdfe, a new Stata command for estimation of
(pseudo) Poisson regression models with multiple high-dimensional fixed effects
(HDFE). Estimation is implemented using a modified version of the iteratively
reweighted least-squares (IRLS) algorithm that allows for fast estimation in
the presence of HDFE. Because the code is built around the reghdfe package, it
has similar syntax, supports many of the same functionalities, and benefits
from reghdfe's fast convergence properties for computing high-dimensional least
squares problems.
Performance is further enhanced by some new techniques we introduce for
accelerating HDFE-IRLS estimation specifically. ppmlhdfe also implements a
novel and more robust approach to check for the existence of (pseudo) maximum
likelihood estimates.Comment: For associated code and data repository, see
https://github.com/sergiocorreia/ppmlhdf
Variance Estimation in a Random Coefficients Model
This papers describes an estimator for a standard state-space model with coefficients generated by a random walk that is statistically superior to the Kalman filter as applied to this particular class of models. Two closely related estimators for the variances are introduced: A maximum likelihood estimator and a moments estimator that builds on the idea that some moments are equalized to their expectations. These estimators perform quite similar in many cases. In some cases, however, the moments estimator is preferable both to the proposed likelihood estimator and the Kalman filter, as implemented in the program package Eviews.time-varying coefficients; adaptive estimation; random walk; Kalman filter; state-space model
Sizes and Temperature Profiles of Quasar Accretion Disks from Chromatic Microlensing
Microlensing perturbations to the flux ratios of gravitationally lensed
quasar images can vary with wavelength because of the chromatic dependence of
the accretion disk's apparent size. Multiwavelength observations of microlensed
quasars can thus constrain the temperature profiles of their accretion disks, a
fundamental test of an important astrophysical process which is not currently
possible using any other method. We present single-epoch broadband flux ratios
for 12 quadruply lensed quasars in eight bands ranging from 0.36 to 2.2
microns, as well as Chandra 0.5--8 keV flux ratios for five of them. We combine
the optical/IR and X-ray ratios, together with X-ray ratios from the
literature, using a Bayesian approach to constrain the half-light radii of the
quasars in each filter. Comparing the overall disk sizes and wavelength slopes
to those predicted by the standard thin accretion disk model, we find that on
average the disks are larger than predicted by nearly an order of magnitude,
with sizes that grow with wavelength with an average slope of ~0.2 rather than
the slope of 4/3 predicted by the standard thin disk theory. Though the error
bars on the slope are large for individual quasars, the large sample size lends
weight to the overall result. Our results present severe difficulties for a
standard thin accretion disk as the main source of UV/optical radiation from
quasars.Comment: 21 pages, 9 tables, 10 figures. Fairly significant changes made to
match published version, including the addition of an extra table, and extra
figure, and some explanatory tex
Principal arc analysis on direct product manifolds
We propose a new approach to analyze data that naturally lie on manifolds. We
focus on a special class of manifolds, called direct product manifolds, whose
intrinsic dimension could be very high. Our method finds a low-dimensional
representation of the manifold that can be used to find and visualize the
principal modes of variation of the data, as Principal Component Analysis (PCA)
does in linear spaces. The proposed method improves upon earlier manifold
extensions of PCA by more concisely capturing important nonlinear modes. For
the special case of data on a sphere, variation following nongeodesic arcs is
captured in a single mode, compared to the two modes needed by previous
methods. Several computational and statistical challenges are resolved. The
development on spheres forms the basis of principal arc analysis on more
complicated manifolds. The benefits of the method are illustrated by a data
example using medial representations in image analysis.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS370 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
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