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Nonparametric estimation of random effects densities in a linear mixed-effects model with Fourier-oscillating noise density

Author

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  • Dang Duc Trong
  • Cao Xuan Phuong
  • Tran Quoc Viet

Abstract

This paper is devoted to the study of nonparametric estimation of random effects densities in a linear mixed-effects model. In the first case where noise distribution is fully known, we apply nonparametric deconvolution tools to construct mean consistent estimators with respect to the L2(R)-error and then study convergence rates of the proposed estimators when noise density is Fourier-oscillating. In the second case where the random noises are assumed to be the uniform distribution on (−a,a) with an unknown a > 0, we propose an estimator for a and then inherit the methodologies in the case of known noise distribution to construct necessary estimators which are also shown to be mean consistency. Some numerical results in the first case of the random noises are presented to illustrate the methodology.

Suggested Citation

  • Dang Duc Trong & Cao Xuan Phuong & Tran Quoc Viet, 2020. "Nonparametric estimation of random effects densities in a linear mixed-effects model with Fourier-oscillating noise density," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 49(24), pages 5988-6015, December.
    • Handle: RePEc:taf:lstaxx:v:49:y:2020:i:24:p:5988-6015
    DOI: 10.1080/03610926.2019.1625923
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