Exponential Bounds and Convergence Rates of Sieve Estimators for Functional Autoregressive Processes

Nesrine Kara Terki () and Tahar Mourid
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Nesrine Kara Terki: Higher School of Management-Tlemcen
Tahar Mourid: University of Abou Bakr Belkaid Tlemcen

Sankhya A: The Indian Journal of Statistics, 2024, vol. 86, issue 1, No 11, 364-391

Abstract: Abstract In the following study, we deal with the exponential bounds and rates for a class of sieve estimators of Grenander for Functional Autoregressive Processes when the parameter operator belongs to the parameter space of Hilbert-Schmidt operators. Two classes of parameter operators are considered where we state clearly sieve estimators formulas and derive corresponding exponential bounds. These results are applied to establish their almost sure convergence and almost complete convergence. Then, we determine rates of convergence of sieve estimators in each class. The numerical studies illustrate the performance of the sieve predictors and give comparisons with other existing prediction methods both on simulated and real functional data sets exhibiting competitive results.

Keywords: Exponential bounds; Functional autoregressive processes; Maximum likelihood estimators (MLE); Rates of convergence (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s13171-023-00322-w

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