175,772 research outputs found
Towards a Hamilton-Jacobi Theory for Nonholonomic Mechanical Systems
In this paper we obtain a Hamilton-Jacobi theory for nonholonomic mechanical
systems. The results are applied to a large class of nonholonomic mechanical
systems, the so-called \v{C}aplygin systems.Comment: 13 pages, added references, fixed typos, comparison with previous
approaches and some explanations added. To appear in J. Phys.
Bias Reduction of Long Memory Parameter Estimators via the Pre-filtered Sieve Bootstrap
This paper investigates the use of bootstrap-based bias correction of
semi-parametric estimators of the long memory parameter in fractionally
integrated processes. The re-sampling method involves the application of the
sieve bootstrap to data pre-filtered by a preliminary semi-parametric estimate
of the long memory parameter. Theoretical justification for using the bootstrap
techniques to bias adjust log-periodogram and semi-parametric local Whittle
estimators of the memory parameter is provided. Simulation evidence comparing
the performance of the bootstrap bias correction with analytical bias
correction techniques is also presented. The bootstrap method is shown to
produce notable bias reductions, in particular when applied to an estimator for
which analytical adjustments have already been used. The empirical coverage of
confidence intervals based on the bias-adjusted estimators is very close to the
nominal, for a reasonably large sample size, more so than for the comparable
analytically adjusted estimators. The precision of inferences (as measured by
interval length) is also greater when the bootstrap is used to bias correct
rather than analytical adjustments.Comment: 38 page
Higher-Order Improvements of the Sieve Bootstrap for Fractionally Integrated Processes
This paper investigates the accuracy of bootstrap-based inference in the case
of long memory fractionally integrated processes. The re-sampling method is
based on the semi-parametric sieve approach, whereby the dynamics in the
process used to produce the bootstrap draws are captured by an autoregressive
approximation. Application of the sieve method to data pre-filtered by a
semi-parametric estimate of the long memory parameter is also explored.
Higher-order improvements yielded by both forms of re-sampling are demonstrated
using Edgeworth expansions for a broad class of statistics that includes first-
and second-order moments, the discrete Fourier transform and regression
coefficients. The methods are then applied to the problem of estimating the
sampling distributions of the sample mean and of selected sample
autocorrelation coefficients, in experimental settings. In the case of the
sample mean, the pre-filtered version of the bootstrap is shown to avoid the
distinct underestimation of the sampling variance of the mean which the raw
sieve method demonstrates in finite samples, higher order accuracy of the
latter notwithstanding. Pre-filtering also produces gains in terms of the
accuracy with which the sampling distributions of the sample autocorrelations
are reproduced, most notably in the part of the parameter space in which
asymptotic normality does not obtain. Most importantly, the sieve bootstrap is
shown to reproduce the (empirically infeasible) Edgeworth expansion of the
sampling distribution of the autocorrelation coefficients, in the part of the
parameter space in which the expansion is valid
Keck Observations of the Hidden Quasar IRAS P09104+4109
We present imaging and spectro- polarimetric observations of the
ultraluminous infrared galaxy IRAS P09104+4109 using the Keck 10-m Telescope.
We detect the clear presence of broad Hb, Hg, and MgII 2800 emission lines in
the polarized flux spectra of the nucleus and of an extranuclear emission
region ~ 4" away, confirming the presence of a hidden central quasar. The
polarization of the broad Mg II emission line is high (~ 29%), consistent with
the remarkably high polarization (~ 30%-40%) observed in the extended continuum
emission. The narrow emission lines are polarized in a stratified fashion, with
the high ionization lines being polarized 0.7%-1.7% and [O II] essentially
unpolarized. The line polarizations are positively correlated with critical
density, ionization potential, and velocity width of the emission lines. This
indicates that the NLR may be partially shadowed by the putative torus, with
the higher ionization lines originating closer to the nucleus. One notable
characteristic of the extranuclear knot is that all species of Fe are markedly
absent in its spectrum, while they appear prominently in the nucleus. Our
favored interpretation is that there is a large amount of dust in the
extranuclear regions, allowing gaseous refractory metals to deposit. The
extended emission regions are most likely material shredded from nearby cluster
members and not gas condensed from the cooling flow or expelled from the
obscured quasar. Our data provide strong evidence for matter-bounded clouds in
addition to ionization-bounded clouds in the NLR. Ionization by pure velocity
shocks can be ruled out. Shocks with photoionizing precursors may be present,
but are probably not a dominant contributor to the energy input.Comment: 32 pages, including 9 figs and 2 tables, to be published in the
Astronomical Journa
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