Authors: Zhicheng Chen
Comments: 6 Pages.
Data loss is a big problem in many online monitoring systems due to various reasons. Copula-based approaches are effective imputation methods for missing data imputation; however, such methods are highly dependent on a reliable distribution of missing data. This article proposed a functional regression approach for missing probability density function (PDF) imputation. PDFs are first transformed to a Hilbert space by the log quantile density (LQD) transformation. The transformed results of the response PDFs are approximated by the truncated Karhunen–Loève representation. Corresponding representation in the Hilbert space of a missing PDF is estimated by a vector-on-function regression model in reproducing kernel Hilbert space (RKHS), then mapping back to the density space by the inverse LQD transformation to obtain an imputation for the missing PDF. To address errors caused by the numerical integration in the inverse LQD transformation, original PDFs are aided by a PDF of uniform distribution. The effect of the added uniform distribution in the imputed result of a missing PDF can be separated by the warping function-based PDF estimation technique.
We present a review of data types and statistical methods often encountered in astronomy. The aim is to provide an introduction to statistical applications in astronomy for statisticians and computer scientists. We highlight the complex, often hierarchical, nature of many astronomy inference problems and advocate for cross-disciplinary collaborations to address these challenges.