Frequentist estimation of cosmological parameters from the MAXIMA-1 cosmic microwave background anisotropy data

We use a frequentist statistical approach to set confidence intervals on the values of cosmological parameters using the MAXIMA-1 and COBE measurements of the angular power spectrum of the cosmic microwave background. We define a Δ_χ² statistic, simulate the measurements of MAXIMA-1 and COBE, determine the probability distribution of the statistic, and use it and the data to set confidence intervals on several cosmological parameters. We compare the frequentist confidence intervals with Bayesian credible regions. The frequentist and Bayesian approaches give best estimates for the parameters that agree within 15 per cent, and confidence interval widths that agree to within 30 per cent. The results also suggest that a frequentist analysis gives slightly broader confidence intervals than a Bayesian analysis. The frequentist analysis gives values of Ω = 0.89^+0.26_-0.19, Ω_B h² = 0.026^+0.020_-0.011 and n = 1.02^+0.31_-0.10 and the Bayesian analysis gives values of Ω = 0.98^+0.14_-0.19, Ω_B h² = 0.029^+0.015_-0.010 and n = 1.18^+0.10_-0.23, all at the 95 per cent confidence level.