Issue |
A&A
Volume 373, Number 1, July I 2001
|
|
---|---|---|
Page(s) | 359 - 368 | |
Section | Numerical methods and codes | |
DOI | https://doi.org/10.1051/0004-6361:20010620 | |
Published online | 15 July 2001 |
Smooth maps from clumpy data
Institüt für Astrophysik und Extraterrestrische Forschung, Universität Bonn, Auf dem Hügel 71, 53121 Bonn, Germany
Corresponding author: M. Lombardi, lombardi@astro.uni-bonn.de
Received:
22
January
2001
Accepted:
12
April
2001
We study an estimator for smoothing irregularly sampled data into a
smooth map. The estimator has been widely used in astronomy, owing
to its low level of noise; it involves a weight function -or
smoothing kernel -. We show that this estimator is
not unbiased, in the sense that the expectation value of the
smoothed map is not the underlying process convolved with w, but a
convolution with a modified kernel
. We
show how to calculate
for a given kernel w and
investigate its properties. In particular, it is found that (1)
is normalized, (2) has a shape "similar" to the
original kernel w, (3) converges to w in the limit of high
number density of data points, and (4) reduces to a top-hat filter
in the limit of very small number density of data points. Hence,
although the estimator is biased, the bias is well understood
analytically, and since
has all the desired
properties of a smoothing kernel, the estimator is in fact very
useful. We present explicit examples for several filter functions
which are commonly used, and provide a series expression valid in
the limit of a large density of data points.
Key words: methods: statistical / methods: analytical / methods: data analysis / gravitational lensing
© ESO, 2001
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