23,518 research outputs found
Some comments on C. S. Wallace's random number generators
We outline some of Chris Wallace's contributions to pseudo-random number
generation. In particular, we consider his idea for generating normally
distributed variates without relying on a source of uniform random numbers, and
compare it with more conventional methods for generating normal random numbers.
Implementations of Wallace's idea can be very fast (approximately as fast as
good uniform generators). We discuss the statistical quality of the output, and
mention how certain pitfalls can be avoided.Comment: 13 pages. For further information, see
http://wwwmaths.anu.edu.au/~brent/pub/pub213.htm
On the estimation of the Lorenz curve under complex sampling designs
This paper focuses on the estimation of the concentration curve of a finite
population, when data are collected according to a complex sampling design with
different inclusion probabilities. A (design-based) Hajek type estimator for
the Lorenz curve is proposed, and its asymptotic properties are studied. Then,
a resampling scheme able to approximate the asymptotic law of the Lorenz curve
estimator is constructed. Applications are given to the construction of (i) a
confidence band for the Lorenz curve, (ii) confidence intervals for the Gini
concentration ratio, and (iii) a test for Lorenz dominance. The merits of the
proposed resampling procedure are evaluated through a simulation study
Approximate Bayesian computation via the energy statistic
Approximate Bayesian computation (ABC) has become an essential part of the
Bayesian toolbox for addressing problems in which the likelihood is
prohibitively expensive or entirely unknown, making it intractable. ABC defines
a pseudo-posterior by comparing observed data with simulated data,
traditionally based on some summary statistics, the elicitation of which is
regarded as a key difficulty. Recently, using data discrepancy measures has
been proposed in order to bypass the construction of summary statistics. Here
we propose to use the importance-sampling ABC (IS-ABC) algorithm relying on the
so-called two-sample energy statistic. We establish a new asymptotic result for
the case where both the observed sample size and the simulated data sample size
increase to infinity, which highlights to what extent the data discrepancy
measure impacts the asymptotic pseudo-posterior. The result holds in the broad
setting of IS-ABC methodologies, thus generalizing previous results that have
been established only for rejection ABC algorithms. Furthermore, we propose a
consistent V-statistic estimator of the energy statistic, under which we show
that the large sample result holds, and prove that the rejection ABC algorithm,
based on the energy statistic, generates pseudo-posterior distributions that
achieves convergence to the correct limits, when implemented with rejection
thresholds that converge to zero, in the finite sample setting. Our proposed
energy statistic based ABC algorithm is demonstrated on a variety of models,
including a Gaussian mixture, a moving-average model of order two, a bivariate
beta and a multivariate -and- distribution. We find that our proposed
method compares well with alternative discrepancy measures.Comment: 25 pages, 6 figures, 5 table
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