Estimating a cosmological mass bias parameter with bootstrap bandwidth selection

Ji Meng Loh, Woncheol Jang

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

We focus on selecting optimal bandwidths for non-parametric estimation of the two-point correlation function of a point pattern. We obtain these optimal bandwidths by using a bootstrap approach to select a bandwidth that minimizes the integrated squared error. The variance term is estimated by using a non-parametric spatial bootstrap, whereas the bias term is estimated with a plug-in approach using a pilot estimator of the two-point correlation function based on a parametric model. The choice of parametric model for the pilot estimator is very flexible. Depending on applications, parametric statistical point models, physical models or functional models can be used. We also explore the use of the procedure for selecting adaptive optimal bandwidths. We investigate the performance of the bandwidth selection procedure by using a simulation study. In our data example, we apply our method to a Sloan Digital Sky Survey galaxy cluster catalogue by using a pilot estimator based on the power law functional model in cosmology. The resulting non-parametric two-point correlation function estimate is then used to estimate a cosmological mass bias parameter that describes the relationship between the galaxy mass distribution and the underlying matter distribution.

Original languageEnglish (US)
Pages (from-to)761-779
Number of pages19
JournalJournal of the Royal Statistical Society. Series C: Applied Statistics
Volume59
Issue number5
DOIs
StatePublished - Nov 1 2010
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Keywords

  • Adaptive bandwidth
  • Bandwidth selection
  • Bootstrap
  • Cosmological models
  • Mass bias parameter
  • Minimum Χ estimation
  • Sloan Digital Sky Survey
  • Two-point correlation function

Fingerprint Dive into the research topics of 'Estimating a cosmological mass bias parameter with bootstrap bandwidth selection'. Together they form a unique fingerprint.

Cite this