The $k$ nearest neighbors local linear estimator of functional conditional density when there are missing data

Abstract

Our key aim is to propose effective estimators for the conditional probability density of a scalar response variable given a functional co-variable, where the response variable is considered to have missing data at random. Such estimators are constructed by combining the approaches of the local linear method and the kernel nearest neighborhood. The main feature of this estimation is the possibility to model the missing phenomena. Under less restrictive conditions, we show the strong consistency of the proposed estimators. To assess the efficacy of the developed estimators, empirical analysis as well as real data analyses are performed.

Keywords

• functional data analysis
• small ball probability
• local linear method
• k nearest neighbors
• conditional density
• almost complete convergence

Supporting Institution

King Khalid University

Project Number

R.G.P.2/68/41.

Thanks

The authors are very grateful to the Deanship of Scientific Research at King Khalid University, Kingdom of Saudi Arabia for supporting and funding this work through the research groups program under the project number R.G.P.2/68/41.

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