Bibcode
Rubiño-Martín, J. A.; Betancort-Rijo, J. E.
Referencia bibliográfica
Monthly Notices of the Royal Astronomical Society, Volume 345, Issue 1, pp. 221-232.
Fecha de publicación:
10
2003
Número de citas
2
Número de citas referidas
2
Descripción
We present a new general procedure for determining a given set of
quantities. To this end, we define a certain statistic, which we call
`modified χ2' (χ2M), because of
its similarity to the standard χ2. The terms of this
χ2M are made up of the fluctuations of an
unbiased estimator of some statistical quantities and certain weights.
Only the diagonal terms of the covariance matrix appear explicitly in
our statistic, while the full covariance matrix (and not its inverse) is
included implicitly in the calculation of the weights. Choosing these
weights, we may obtain, through minimizing
χ2M, the estimator that provides the minimum
rms, either for those quantities or for the parameters on which these
quantities depend. In this paper, we describe our method in the context
of cosmic microwave background experiments, in order to obtain either
the statistical properties of the maps or the cosmological parameters.
The test here is constructed out of some estimator of the two-point
correlation function at different angles. For the problem of
one-parameter estimation, we show that our method has the same power as
the maximum-likelihood method. We have also applied this method to Monte
Carlo simulations of the COBE-DMR data, as well as to the actual 4-yr
data, obtaining consistent results with previous analyses. We also
provide a very good analytical approximation to the distribution
function of our statistic, which could also be useful in other contexts.