$ k $NN local linear estimation of the conditional density and mode for functional spatial high dimensional data

Fatimah Alshahrani; Wahiba Bouabsa; Ibrahim M. Almanjahie; Mohammed Kadi Attouch; Fatimah Alshahrani; Wahiba Bouabsa; Ibrahim M. Almanjahie; Mohammed Kadi Attouch

doi:10.3934/math.2023809

AIMS Mathematics

2023, Volume 8, Issue 7: 15844-15875. doi: 10.3934/math.2023809

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Research article

$ k $NN local linear estimation of the conditional density and mode for functional spatial high dimensional data

1.
Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, Riyadh 11671, Saudi Arabia
2.
Laboratory of Statistics and Stochastic Processes, University of Djillali Liabes, BP 89, Sidi Bel Abbes 22000, Algeria
3.
Department of Mathematics, College of Science, King Khalid University, Abha 62223, Saudi Arabia

Received: 12 January 2023 Revised: 02 April 2023 Accepted: 11 April 2023 Published: 04 May 2023
MSC : 62H12, 62G07, 62G35, 62G20

Traditionally, regression problems are examined using univariate characteristics, including the scale function, marginal density, regression error, and regression function. When the correlation between the response and the predictor is reasonably straightforward, these qualities are helpful and instructive. Given the predictor, the response's conditional density provides more specific information regarding the relationship. This study aims to examine a nonparametric estimator of a scalar response variable's function of a density and mode, given a functional variable when the data are spatially dependent. The estimator is then derived and established by combining the local linear and the $ k $ nearest neighbors methods. Next, the suggested estimator's uniform consistency in the number of neighbors (UNN) is proved. Finally, to demonstrate the efficacy and superiority of the acquired results, we applied our new estimator to simulated and real data and compared it to the existing competing estimator.
- $ k $ nearest neighbors,
- spatial functional data analysis,
- local linear estimation,
- conditional density,
- conditional mode
Citation: Fatimah Alshahrani, Wahiba Bouabsa, Ibrahim M. Almanjahie, Mohammed Kadi Attouch. $ k $NN local linear estimation of the conditional density and mode for functional spatial high dimensional data[J]. AIMS Mathematics, 2023, 8(7): 15844-15875. doi: 10.3934/math.2023809

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Abstract

Traditionally, regression problems are examined using univariate characteristics, including the scale function, marginal density, regression error, and regression function. When the correlation between the response and the predictor is reasonably straightforward, these qualities are helpful and instructive. Given the predictor, the response's conditional density provides more specific information regarding the relationship. This study aims to examine a nonparametric estimator of a scalar response variable's function of a density and mode, given a functional variable when the data are spatially dependent. The estimator is then derived and established by combining the local linear and the $ k $ nearest neighbors methods. Next, the suggested estimator's uniform consistency in the number of neighbors (UNN) is proved. Finally, to demonstrate the efficacy and superiority of the acquired results, we applied our new estimator to simulated and real data and compared it to the existing competing estimator.

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