On kernel estimators of density ratio

Sy Mien Chen, Yu Sheng Hsu, Jian Tong Liaw

Research output: Contribution to journalArticlepeer-review

18 Scopus citations


Let f (x) and g(x) denote two probability density functions and g(x) ≠ 0. There are two ways to estimate the density ratio f (x)/g(x). One is to estimate f (x) and g(x) first and then the ratio, the other is to estimate f (x)/g(x) directly. In this paper, we derive asymptotic mean square errors and central limit theorems for both estimators.

Original languageEnglish
Pages (from-to)463-479
Number of pages17
Issue number5
StatePublished - Oct 2009


  • Central limit theorem
  • Density ratio
  • Kernel estimators
  • Mean square error


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