Astronomy and Astrophysics – Astrophysics
Scientific paper
Jun 1992
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1992apj...392..452m&link_type=abstract
Astrophysical Journal, Part 1 (ISSN 0004-637X), vol. 392, no. 2, June 20, 1992, p. 452-457. Research supported by Max-Planck-Ins
Astronomy and Astrophysics
Astrophysics
101
Digital Simulation, Error Analysis, Galactic Clusters, Statistical Correlation, Astronomical Models, Regression Analysis
Scientific paper
Analytical formulas are derived for ensemble and bootstrap-resampling errors in two- and three-point correlation functions xi and zeta. The analytical results agree with numerical simulations. Similar derivations are carried out for sparse-sampling errors as well. The fit errors of the parameters (i.e., the amplitude A of xi and the constant Q of zeta) in the regression models are also discussed. The interdependence among the counts in different bins reduces the fit errors. If the ensemble errors sigma-DD(ens) and sigma-DDD(ens) are adopted for the counts, the fit errors of A and Q in each sample are about half of the standard errors obtained from the ensemble of samples. The underestimation of the fit errors due to the bin-bin interdependence is compensated by the overestimation of sigma-DD and sigma-DDD given by the bootstrap-resampling method. The fit errors of the parameters, given by the bootstrap-resampling errors of the counts, give the correct answers.
Boerner Gerhard
Jing Yi-Peng
Mo Hou-Jun
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