FDA: theoretical and practical efficiency of the local linear estimation based on the kNN smoothing of the conditional distribution when there are missing data

ABSTRACT

We aim to estimate effectively the conditional distribution function (CDF) of a scalar response variable, with missing data at random, given a functional co-variable. For this aim, we combine the local linear approach with the kernel nearest neighbours procedure to construct a new estimator of the CDF. A fundamental issue of interest is to study the impact of the missing observations on the performances of estimators. We establish, under less restrictive conditions, the strong consistency of the constructed estimator. Then, we test first its effectiveness on simulated and real datasets, and then we conclude by a comparison study with classical estimators of the CDF.

KEYWORDS:

• Functional data analysis (FDA)
• nonparametric functional data analysis (NFDA)
• almost-complete convergence (a.co.)
• local linear estimation (LLE)
• conditional distribution function (CDF)
• k-nearest neighbours (kNN) method
• missing data at random (MAR)

AMS SUBJECT CLASSIFICATIONS:

• 62G05
• 62G08
• 62G20
• 62G35
• 62G07
• 62G32
• 62G30
• Secondary: 62E20

Acknowledgements

The authors would like to thank the Associate Editor and two anonymous reviewers for their valuable comments and suggestions which improved substantially the quality of this paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Mustapha Rachdi http://orcid.org/0000-0002-9203-056X

Additional information

Funding

The authors extend their appreciation to the Deanship of Scientific Research at King Khalid University for funding this work through General Research Project under grant number: G.R.P-90-41.