Tail- or boundary-bias-free nonparametric direct density ratio estimation and its application

2020 Fiscal Year Final Research Report

• Project/Area Number: 17K13714
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Economic statistics
• Research Institution: University of Tsukuba
• Principal Investigator: Igarashi Gaku 筑波大学, システム情報系, 助教 (40759346)
• Project Period (FY): 2017-04-01 – 2021-03-31
• Keywords: ノンパラメトリック密度比推定

Outline of Final Research Achievements

We focused on direct probability density ratio estimation, which directly estimates the ratio of probability density function nonparametrically. We proposed a probability density ratio estimator, which is free of tail or boundary bias, using the beta kernel. We also studied methods of selecting smoothing parameter which control the smoothness of the estimator, and proposed a method by the leave-one-out cross-validation. Furthermore, we also proposed a nonparametric discontinuity test of probability density using the direct beta kernel probability density ratio estimator as the test statistic, and a smoothing parameter selection method for the test. We showed that the power of the proposed test is large when used as a one-tailed test.

Free Research Field

統計科学

Academic Significance and Societal Importance of the Research Achievements

確率密度関数の比（確率密度比）は、条件付き確率密度推定や、異常値検出などの2標本検定に用いられる。裾・境界バイアスのない確率密度比推定は、裾・境界における推定・検定精度の向上に役立つと考えられる。また、確率密度の不連続性検定は回帰不連続デザインの条件確認等に用いられ、直接型ベータカーネル確率密度比推定量を用いた検定は、片側検定の際に精度が向上が期待できる。