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**A Non-parametric Analysis of the CMB Power Spectrum**

**Christopher J. Miller, Robert C. Nichol, Christopher Genovese
and Larry Wasserman**

### Abstract:

We examine Cosmic Microwave Background (CMB) temperature power spectra from
the BOOMERANG, MAXIMA, and DASI experiments.
We non-parametrically estimate the true power spectrum with no model assumptions.
This is a significant departure
from previous research which used either cosmological models or
some other parameterized form (e.g. parabolic fits).
Our non-parametric estimate is practically
indistinguishable from the best fit cosmological model,
thus lending independent support to the underlying physics
that governs these models.
We also generate a confidence set for the non-parametric fit and extract
confidence intervals for the numbers, locations, and heights
of peaks and the successive peak-to-peak height ratios.
At the 95%, 68%, and 40% confidence levels, we find functions that fit
the data with
one, two, and three peaks respectively
().
Therefore, the current data prefer two peaks
at the level.
If we assume that there are three peaks in the data, we find
their locations to be within = (118,300), = (377,650),
and = (597,900). We find the ratio of the first peak-height
to the second and the second to the third .All measurements are for 95% confidence.
If the standard errors on the temperature measurements were
reduced to a third of what they are currently,
as we expect to be achieved
by the MAP and Planck CMB experiments,
we could eliminate two-peak models at the 95% confidence limit.
The non-parametric methodology discussed in this paper has many
astrophysical applications.

*Heidi Sestrich*

*9/18/2001*
Here is the full text for this
technical report as a .pdf file.