A flexible method for estimating luminosity functions via Kernel Density Estimation

dc.contributor.authorJarvis, Matt J.
dc.contributor.authorYuan, Zunli
dc.contributor.authorWang, Jiancheng
dc.date.accessioned2021-02-17T11:53:43Z
dc.date.available2021-02-17T11:53:43Z
dc.date.issued2020
dc.description.abstractWe propose a flexible method for estimating luminosity functions (LFs) based on kernel density estimation (KDE), the most popular nonparametric density estimation approach developed in modern statistics, to overcome issues surrounding binning of LFs. One challenge in applying KDE to LFs is how to treat the boundary bias problem, since astronomical surveys usually obtain truncated samples predominantly due to the flux-density limits of surveys. We use two solutions, the transformation KDE method (φˆ t), and the transformation-reflection KDE method (φˆ tr) to reduce the boundary bias. We develop a new likelihood cross-validation criterion for selecting optimal bandwidths, based on which, the posterior probability distribution of bandwidth and transformation parameters for φˆ t and φˆ tr are derived within a Markov chain Monte Carlo (MCMC) sampling procedure. The simulation result shows that φˆ t and φˆ tr perform better than the traditional binned method, especially in the sparse data regime around the flux-limit of a survey or at the bright-end of the LF. To further improve the performance of our KDE methods, we develop the transformation-reflection adaptive KDE approach (φˆ tra). Monte Carlo simulations suggest that it has a good stability and reliability in performance, and is around an order of magnitude more accurate than using the binned method. By applying our adaptive KDE method to a quasar sample, we find that it achieves estimates comparable to the rigorous determination in a previous work, while making far fewer assumptions about the LF. The KDE method we develop has the advantages of both parametric and non-parametric methods.en_US
dc.identifier.citationJarvis, M. J. et al. (2020). A flexible method for estimating luminosity functions via Kernel Density Estimation. The Astrophysical Journal Supplement Series, 248(1)en_US
dc.identifier.uri10.3847/1538-4365/ab855b
dc.identifier.urihttp://hdl.handle.net/10566/5951
dc.language.isoenen_US
dc.publisherIOP Publishingen_US
dc.subjectMethods: data analysisen_US
dc.subjectMethods: statisticalen_US
dc.subjectGalaxies: luminosity functionen_US
dc.subjectMass functionen_US
dc.subjectRedshiften_US
dc.titleA flexible method for estimating luminosity functions via Kernel Density Estimationen_US
dc.typeArticleen_US

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