CMB bispectrum, trispectrum, non-Gaussianity, and the Cramer-Rao bound

Journal Article · Sat Jan 15 04:00:00 EST 2011 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.83.023007· OSTI ID:21503925

Kamionkowski, Marc; Smith, Tristan L; Heavens, Alan ^[1]

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1. California Institute of Technology, Mail Code 350-17, Pasadena, California 91125 (United States)

Minimum-variance estimators for the parameter f{sub nl} that quantifies local-model non-Gaussianity can be constructed from the cosmic microwave background (CMB) bispectrum (three-point function) and also from the trispectrum (four-point function). Some have suggested that a comparison between the estimates for the values of f{sub nl} from the bispectrum and trispectrum allow a consistency test for the model. But others argue that the saturation of the Cramer-Rao bound--which gives a lower limit to the variance of an estimator--by the bispectrum estimator implies that no further information on f{sub nl} can be obtained from the trispectrum. Here, we elaborate the nature of the correlation between the bispectrum and trispectrum estimators for f{sub nl}. We show that the two estimators become statistically independent in the limit of large number of CMB pixels, and thus that the trispectrum estimator does indeed provide additional information on f{sub nl} beyond that obtained from the bispectrum. We explain how this conclusion is consistent with the Cramer-Rao bound. Our discussion of the Cramer-Rao bound may be of interest to those doing Fisher-matrix parameter-estimation forecasts or data analysis in other areas of physics as well.

• OSTI ID: 21503925
• Journal Information: Physical Review. D, Particles Fields, Journal Name: Physical Review. D, Particles Fields Journal Issue: 2 Vol. 83; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
73 NUCLEAR PHYSICS AND RADIATION PHYSICS
COMPARATIVE EVALUATIONS
CORRELATIONS
DATA ANALYSIS
ELECTROMAGNETIC RADIATION
ENERGY SPECTRA
EVALUATION
MICROWAVE RADIATION
RADIATIONS
RELICT RADIATION
SATURATION
SIMULATION
SPECTRA