15,309 research outputs found
On characterising the variability properties of X-ray light curves from active galaxies
We review some practical aspects of measuring the amplitude of variability in
`red noise' light curves typical of those from Active Galactic Nuclei (AGN).
The quantities commonly used to estimate the variability amplitude in AGN light
curves, such as the fractional rms variability amplitude, F_var, and excess
variance, sigma_XS^2, are examined. Their statistical properties, relationship
to the power spectrum, and uses for investigating the nature of the variability
processes are discussed. We demonstrate that sigma_XS^2 (or similarly F_var)
shows large changes from one part of the light curve to the next, even when the
variability is produced by a stationary process. This limits the usefulness of
these estimators for quantifying differences in variability amplitude between
different sources or from epoch to epoch in one source. Some examples of the
expected scatter in the variance are tabulated for various typical power
spectral shapes, based on Monte Carlo simulations. The excess variance can be
useful for comparing the variability amplitudes of light curves in different
energy bands from the same observation. Monte Carlo simulations are used to
derive a description of the uncertainty in the amplitude expected between
different energy bands (due to measurement errors). Finally, these estimators
are used to demonstrate some variability properties of the bright Seyfert 1
galaxy Markarian 766. The source is found to show a strong, linear correlation
between rms amplitude and flux, and to show significant spectral variability.Comment: 14 pages. 12 figures. Accepted for publication in MNRA
Symmetrically normalized instrumental-variable estimation using panel data
In this paper we discuss the estimation of panel data models with sequential moment restrictions using symmetrically normalized GMM estimators. These estimators are asymptotically equivalent to standard GMM but are invariant to normalization and tend to have a smaller finite sample bias. They also have a very different behaviour compared to standard GMM when the instruments are poor. We study the properties of SN-GMM estimators in relation to GMM, minimum distance and pseudo maximum likelihood estimators for various versions of the AR(1) model with individual effects by mean of simulations. The emphasis is not in assessing the value of enforcing particular restrictions in the model; rather, we wish to evaluate the effects in small samples of using alternative estimating criteria that produce asymptotically equivalent estimators for fixed T and large N. Finally, as an empírical illustration, we estimate by SN-GMM employment and wage equations using panels of UK and Spanish firms
Selection Procedures for Order Statistics in Empirical Economic Studies
In a presentation to the American Economics Association, McCloskey (1998) argued that "statistical significance is bankrupt" and that economists' time would be "better spent on finding out How Big Is Big". This brief survey is devoted to methods of determining "How Big Is Big". It is concerned with a rich body of literature called selection procedures, which are statistical methods that allow inference on order statistics and which enable empiricists to attach confidence levels to statements about the relative magnitudes of population parameters (i.e. How Big Is Big). Despite their prolonged existence and common use in other fields, selection procedures have gone relatively unnoticed in the field of economics, and, perhaps, their use is long overdue. The purpose of this paper is to provide a brief survey of selection procedures as an introduction to economists and econometricians and to illustrate their use in economics by discussing a few potential applications. Both simulated and empirical examples are provided.Ranking and selection, multiple comparisons, hypothesis testing
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