Oracle inequalities and adaptive wavelet estimations for a mixture density model

Kaikai Cao; Kaikai Cao

doi:10.3934/math.20261139

AIMS Mathematics

2026, Volume 11, Issue 9: 28628-28645. doi: 10.3934/math.20261139

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Research article

Oracle inequalities and adaptive wavelet estimations for a mixture density model

Kaikai Cao ^,

School of Mathematics and Statistics, Weifang University, Weifang 261061, China

Received: 18 July 2026 Revised: 24 August 2026 Accepted: 01 September 2026 Published: 07 September 2026
MSC : 42C40, 62G07, 62G20

This paper proposes a data-driven wavelet estimator for a mixture density model, in the spirit of the Goldenshluger and Lepski method. In addition, we investigate the fully adaptive estimations for multivariate density functions. First, a pointwise oracle inequality is given, which does not require any assumptions on the underlying function. Moreover, the pointwise estimation under the local Hölder condition and $ L^p $ risk ($ 1\leq p < \infty $) estimations on Besov spaces are investigated, respectively.
- wavelet,
- nonparametric estimation,
- mixture model,
- density function,
- data-driven
Citation: Kaikai Cao. Oracle inequalities and adaptive wavelet estimations for a mixture density model[J]. AIMS Mathematics, 2026, 11(9): 28628-28645. doi: 10.3934/math.20261139

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Abstract

This paper proposes a data-driven wavelet estimator for a mixture density model, in the spirit of the Goldenshluger and Lepski method. In addition, we investigate the fully adaptive estimations for multivariate density functions. First, a pointwise oracle inequality is given, which does not require any assumptions on the underlying function. Moreover, the pointwise estimation under the local Hölder condition and $ L^p $ risk ($ 1\leq p < \infty $) estimations on Besov spaces are investigated, respectively.

References

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