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Nonparametric Estimation in a Nonlinear Time-Varying Generalized Regression Model with Locally Stationary Covariate and ARCH-Errors

Abderrahim Bourhattas & Naâmane Laïb

Mathematical Methods of Statistics2025https://doi.org/10.3103/s1066530724600398article
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This paper focuses on a nonparametric estimation in nonlinear time-varying generalized regression model of order $$d>1$$ , considering locally stationary covariates and autoregressive conditional heteroskedasticity (ARCH) errors. We establish the uniform almost sure convergence rate for the conditional mean and variance functions, under assumptions of local stationarity and local ergodicity. The results are derived without assuming any specific usual type of mixing conditions or physical dependence measure on the data, making them applicable to a diverse range of dependent processes, including those satisfying strong mixing conditions.

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https://doi.org/https://doi.org/10.3103/s1066530724600398

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@article{abderrahim2025,
  title        = {{Nonparametric Estimation in a Nonlinear Time-Varying Generalized Regression Model with Locally Stationary Covariate and ARCH-Errors}},
  author       = {Abderrahim Bourhattas & Naâmane Laïb},
  journal      = {Mathematical Methods of Statistics},
  year         = {2025},
  doi          = {https://doi.org/https://doi.org/10.3103/s1066530724600398},
}

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Nonparametric Estimation in a Nonlinear Time-Varying Generalized Regression Model with Locally Stationary Covariate and ARCH-Errors

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F · citation impact0.50 × 0.4 = 0.20
M · momentum0.50 × 0.15 = 0.07
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R · text relevance †0.50 × 0.4 = 0.20

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