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Estimating parameters of fluctuations in the cosmic microwave background

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  • Tenorio, Luis
  • Lineweaver, Charles H.
  • Smoot, Georges

Abstract

We address questions that arise in statistical analyses of recently detected fluctuations in the Cosmic Microwave Background (CMB). Estimators of the quadrupole amplitude, Q, and spectral index, n, of the CMB angular fluctuation power spectrum are considered. Families of unbiased estimators of Q2 and existence conditions for minimum variance estimators of n are given. We find that the common practice of excluding the quadrupole is not recommended if one is interested in unbiased estimators. We explain previousiy reported correlations of the estimators and show how they depend on the multiple used to normalize the spectrum. We show that a finite beam resolution does not justify the use of truncated least-squares to estimate harmonic coefficients of CMB data.

Suggested Citation

  • Tenorio, Luis & Lineweaver, Charles H. & Smoot, Georges, 1995. "Estimating parameters of fluctuations in the cosmic microwave background," DES - Working Papers. Statistics and Econometrics. WS 4511, Universidad Carlos III de Madrid. Departamento de Estadística.
    • Handle: RePEc:cte:wsrepe:4511
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    Keywords

    Unbiased estimators;

    Statistics

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