A generalization of the moving mean^∗

^∗Space Telescope Science Institute is operated by AURA, Inc. for NASA under contract NAS5-26555.

Abstract

We have extended the concept of the moving mean in two ways. We first show how to incorporate nearby points, in a natural way, that automatically determines the weight function. This weighting can also probe all scale-lengths of the data. We further extend this to include both isotropic and anisotropic sampling in N-dimensional space. We also generalize to include alternative weightings, specified by the user of the technique, and solve the generalN-dimensional, isotropic problem. We make no unverifiable assumptions regarding the errors of observation nor of the form of the moving mean. A numerical example is included too.

Keywords:

• Statistics
• Data analysis
• Moving average
• Smoothing

^∗Space Telescope Science Institute is operated by AURA, Inc. for NASA under contract NAS5-26555.

^†On leave from Torino Observatory.

^‡Affiliated with the Astrophysics Division, Space Science Department, ESA.

^∗Space Telescope Science Institute is operated by AURA, Inc. for NASA under contract NAS5-26555.

^†On leave from Torino Observatory.

^‡Affiliated with the Astrophysics Division, Space Science Department, ESA.

Notes

^∗Space Telescope Science Institute is operated by AURA, Inc. for NASA under contract NAS5-26555.

^†On leave from Torino Observatory.

^‡Affiliated with the Astrophysics Division, Space Science Department, ESA.

Additional information

Notes on contributors

M.G. Lattanzi

† ‡