2022 Fiscal Year Final Research Report
A study on nonparametric inference using asymmetric kernel and its application
| Project/Area Number |
20K11700
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Review Section |
Basic Section 60030:Statistical science-related
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| Research Institution | Hokkaido University |
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Principal Investigator |
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| Project Period (FY) |
2020-04-01 – 2023-03-31
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| Keywords | ノンパラメトリック法 / 密度推定 |
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| Outline of Final Research Achievements |
In this study, we mainly focus on asymptotic theory of boundary-bias-free asymmetric kernel method. Especially, we have proposed (i) a family of Birnbaum-Saunders (BS) type kernels to estimate the probability density function of univariate (or multivariate) nonnegative data and (ii) non-recursive or recursive asymmetric kernel density estimator using the BS type kernels. We have established some desirable asymptotic properties (bias, variance, mean squared error, mean integrated squared error, strong consistency, and asymptotic normality) of various proposed density estimators. Furthermore, we have started with new studies on (iii) density estimation under a certain biased sampling scheme and (iv) higher-order density derivatives estimation of nonnegative data. We also have conducted the simulation studies to confirm some theoretical results.
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| Free Research Field |
統計科学、数理統計学
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| Academic Significance and Societal Importance of the Research Achievements |
ノンパラメトリック関数推定の題材において、非負データの場合に起こりうる境界バイアスを回避する１つの策として、非対称カーネル法の研究に従事した。個別的な非対称カーネルではなく、カーネル族としての体系化を念頭に置いており、(i)単変量に留まらず、多変量データに適用可能な相関構造も考慮したカーネル族の提案、(ii)逐次的にデータが得られるような場合、計算面で有利な再帰的な非対称カーネル法の提案を含む。また、(iii)バイアス・サンプリングを考慮した推測問題、及び、(iv)密度推定に留まらず、関連した種々の関数推定問題の研究を開始しており、今後、これら方面からの展開が期待される。
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