On the local linear modelization of the conditional density for functional and ergodic data. (English) Zbl 1452.62262
Summary: In this paper, we estimate the conditional density function using the local linear approach. We treat the case when the regressor is valued in a semi-metric space, the response is a scalar and the data are observed as ergodic functional times series. Under this dependence structure, we state the almost complete consistency (a.co.) with rates of the constructed estimator. Moreover, the usefulness of our results is illustrated through their application to the conditional mode estimation.
MSC:
| 62G07 | Density estimation |
| 62G05 | Nonparametric estimation |
| 62G08 | Nonparametric regression and quantile regression |
| 62G20 | Asymptotic properties of nonparametric inference |
| 62G35 | Nonparametric robustness |
| 62H12 | Estimation in multivariate analysis |
| 62M10 | Time series, auto-correlation, regression, etc. in statistics (GARCH) |
| 62R10 | Functional data analysis |
| 62P12 | Applications of statistics to environmental and related topics |
Keywords:
ergodic data; functional data; local linear estimator; conditional density; nonparametric estimation; conditional mode; ozone concentrationReferences:
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