Abstract
We study the asymptotic behavior of the nonparametric local linear estimation of the conditional density of a scalar response variable given a random variable taking values in a semi-metric space. Under some general conditions on the mixing property of the data, we establish the pointwise almost-complete convergence, with rates, of this estimator. Moreover, we give some particular cases of our results which can also be considered as novel in the finite dimensional setting: Nadaraya-Watson estimator, multivariate data and the independent and identically distributed data case. On the other hand, this approach is also applied in time-series analysis to the prediction problem via the conditional mode estimation.
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Demongeot, J., Laksaci, A., Madani, F., Rachdi, M. (2011). A Fast Functional Locally Modeled Conditional Density and Mode for Functional Time-Series. In: Ferraty, F. (eds) Recent Advances in Functional Data Analysis and Related Topics. Contributions to Statistics. Physica-Verlag HD. https://doi.org/10.1007/978-3-7908-2736-1_13
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DOI: https://doi.org/10.1007/978-3-7908-2736-1_13
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