Nonparametric estimation of the measure of functional dependence

Qingsong Shan; Qianning Liu; Qingsong Shan; Qianning Liu

doi:10.3934/math.2021782

AIMS Mathematics

2021, Volume 6, Issue 12: 13488-13502. doi: 10.3934/math.2021782

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Research article

Nonparametric estimation of the measure of functional dependence

Qingsong Shan ,
Qianning Liu ^,

Department of Statistics, Jiangxi University of Finance and Economics, Nanchang, China

Received: 13 May 2021 Accepted: 15 September 2021 Published: 18 September 2021
MSC : 62G05, 62G07

In this paper, we propose a beta kernel estimator to measure functional dependence (MFD). The MFD not only can measure the strength of linear or monotonic relationships, but it is also suitable for more complicated functional dependence. We derive the asymptotic distribution of the proposed estimator and then use several simulated examples to compare our estimator with the traditional measures. Our simulation results demonstrate that beta kernel provides high accuracy in estimation. A real data example is also given to illustrate one possible application of the new estimator.
- mutual complete dependence,
- beta kernel,
- functional dependence,
- monparametric estimation,
- copula
Citation: Qingsong Shan, Qianning Liu. Nonparametric estimation of the measure of functional dependence[J]. AIMS Mathematics, 2021, 6(12): 13488-13502. doi: 10.3934/math.2021782

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Abstract

In this paper, we propose a beta kernel estimator to measure functional dependence (MFD). The MFD not only can measure the strength of linear or monotonic relationships, but it is also suitable for more complicated functional dependence. We derive the asymptotic distribution of the proposed estimator and then use several simulated examples to compare our estimator with the traditional measures. Our simulation results demonstrate that beta kernel provides high accuracy in estimation. A real data example is also given to illustrate one possible application of the new estimator.

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