2,555 research outputs found
Estimates of heterogeneity (I2) can be biased in small meta-analyses
In meta-analysis, the fraction of variance that is due to heterogeneity is
known as I2. We show that the usual estimator of I2 is biased. The bias is
largest when a meta-analysis has few studies and little heterogeneity. For
example, with 7 studies and the true value of I2 at 0, the average estimate of
I2 is .124. Estimates of I2 should be interpreted cautiously when the
meta-analysis is small and the null hypothesis of homogeneity (I2=0) has not
been rejected. In small meta-analyses, confidence intervals may be preferable
to point estimates for I2.Comment: 7 pages + 3 figure
Magnetospherically-trapped dust and a possible model for the unusual transits at WD 1145+017
The rapidly evolving dust and gas extinction observed towards WD 1145+017 has
opened a real-time window onto the mechanisms for destruction-accretion of
planetary bodies onto white dwarf stars, and has served to underline the
importance of considering the dynamics of dust particles around such objects.
Here it is argued that the interaction between (charged) dust grains and the
stellar magnetic field is an important ingredient in understanding the physical
distribution of infrared emitting particles in the vicinity of such white
dwarfs. These ideas are used to suggest a possible model for WD 1145+017 in
which the unusual transit shapes are caused by opaque clouds of dust trapped in
the stellar magnetosphere. The model can account for the observed transit
periodicities if the stellar rotation is near 4.5 h, as the clouds of trapped
dust are then located near or within the co-rotation radius. The model requires
the surface magnetic field to be at least around some tens of kG. In contrast
to the eccentric orbits expected for large planetesimals undergoing tidal
disintegration, the orbits of magnetospherically-trapped dust clouds are
essentially circular, consistent with the observations.Comment: 5 pages, accepted to MNRAS Letter
Constraining the Surface Inhomogeneity and Settling Times of Metals on Accreting White Dwarfs
Due to the short settling times of metals in DA white dwarf atmospheres, any
white dwarfs with photospheric metals must be actively accreting. It is
therefore natural to expect that the metals may not be deposited uniformly on
the surface of the star. We present calculations showing how the temperature
variations associated with white dwarf pulsations lead to an observable
diagnostic of the surface metal distribution, and we show what constraints
current data sets are able to provide. We also investigate the effect that
time-variable accretion has on the metal abundances of different species, and
we show how this can lead to constraints on the gravitational settling times.Comment: 4 pages, 5 figures, accepted for publication in the Astrophysical
Journal Letters, updated reference
Better estimates from binned income data: Interpolated CDFs and mean-matching
Researchers often estimate income statistics from summaries that report the
number of incomes in bins such as \$0-10,000, \$10,001-20,000,...,\$200,000+.
Some analysts assign incomes to bin midpoints, but this treats income as
discrete. Other analysts fit a continuous parametric distribution, but the
distribution may not fit well.
We fit nonparametric continuous distributions that reproduce the bin counts
perfectly by interpolating the cumulative distribution function (CDF). We also
show how both midpoints and interpolated CDFs can be constrained to reproduce
the mean of income when it is known.
We compare the methods' accuracy in estimating the Gini coefficients of all
3,221 US counties. Fitting parametric distributions is very slow. Fitting
interpolated CDFs is much faster and slightly more accurate. Both interpolated
CDFs and midpoints give dramatically better estimates if constrained to match a
known mean.
We have implemented interpolated CDFs in the binsmooth package for R. We have
implemented the midpoint method in the rpme command for Stata. Both
implementations can be constrained to match a known mean.Comment: 20 pages (including Appendix), 3 tables, 2 figures (+2 in Appendix
New Confidence Intervals and Bias Comparisons Show that Maximum Likelihood Can Beat Multiple Imputation in Small Samples
When analyzing incomplete data, is it better to use multiple imputation (MI)
or full information maximum likelihood (ML)? In large samples ML is clearly
better, but in small samples ML's usefulness has been limited because ML
commonly uses normal test statistics and confidence intervals that require
large samples. We propose small-sample t-based ML confidence intervals that
have good coverage and are shorter than t-based confidence intervals under MI.
We also show that ML point estimates are less biased and more efficient than MI
point estimates in small samples of bivariate normal data. With our new
confidence intervals, ML should be preferred over MI, even in small samples,
whenever both options are available.Comment: 5 table
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