Abstract
This study focuses on the nonparametric estimation of the conditional density of a scalar response variable given a random variable taking values in separable Hilbert space. We establish under general conditions the almost complete convergence rates of the conditional density estimator under α-mixing dependence, based on the single-index structure. We also demonstrate the impact of this functional parameter on the mode estimation. Finally, the estimation of the functional index via the pseudo-maximum likelihood method is discussed but not tackled.
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Attaoui, S. On the Nonparametric Conditional Density and Mode Estimates in the Single Functional Index Model with Strongly Mixing Data. Sankhya A 76, 356–378 (2014). https://doi.org/10.1007/s13171-014-0051-6
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DOI: https://doi.org/10.1007/s13171-014-0051-6
Keywords and phrases.
- Conditional density estimation
- Conditional mode estimation
- Functional Hilbert spaces
- Single-index model
- α-mixing dependency.