Cosmological Parameter Estimation: Method

CMB anisotropy data could put powerful constraints on theories of the evolution of our Universe. Using the observations of the large number of CMB experiments, many studies have put constraints on cosmological parameters assuming different frameworks. Assuming for example inflationary paradigm, one can compute the confidence intervals on the different components of the energy densities, or the age of the Universe, inferred by the current set of CMB observations. The aim of this note is to present some of the available methods to derive the cosmological parameters with their confidence intervals from the CMB data, as well as some practical issues to investigate large number of parameters

Self-consistent method for density estimation

The estimation of a density profile from experimental data points is a challenging problem, usually tackled by plotting a histogram. Prior assumptions on the nature of the density, from its smoothness to the specification of its form, allow the design of more accurate estimation procedures, such as Maximum Likelihood. Our aim is to construct a procedure that makes no explicit assumptions, but still providing an accurate estimate of the density. We introduce the self-consistent estimate: the power spectrum of a candidate density is given, and an estimation procedure is constructed on the assumption, to be released \emph{a posteriori}, that the candidate is correct. The self-consistent estimate is defined as a prior candidate density that precisely reproduces itself. Our main result is to derive the exact expression of the self-consistent estimate for any given dataset, and to study its properties. Applications of the method require neither priors on the form of the density nor the subjective choice of parameters. A cutoff frequency, akin to a bin size or a kernel bandwidth, emerges naturally from the derivation. We apply the self-consistent estimate to artificial data generated from various distributions and show that it reaches the theoretical limit for the scaling of the square error with the dataset size.Comment: 21 pages, 5 figure

BER estimation for wireless links using BPSK/QPSK modulation

This paper introduces a method that computes an estimation of the bit error rate (BER) based on the RAKE receiver soft output only. For this method no knowledge is needed about the channel characteristics nor the precise external conditions. Simulations show that the mean error of the estimation is below 2%, with only a small variance. Also an estimation of the BER for a different spreading factor or a different number of RAKE finger can be made. Implementation issues for a practical use of the method are discussed