Estimating the Conditional Density in Scalar-On-Function Regression Structure: k-N-N Local Linear Approach

Abstract

In this study, the problem of conditional density estimation of a scalar response variable, given a functional covariable, is considered. A new estimator is proposed by combining the k-nearest neighbors (k-N-N) procedure with the local linear approach. Then, the uniform consistency in the number of neighbors (UNN) of the proposed estimator is established. Such result is useful in the study of some data-driven rules. As a direct application and consequence of the conditional density estimation, we derive the UNN consistency of the conditional mode function estimator. Finally, to highlight the efficiency and superiority of the obtained results, we applied our new estimator to real data and compare it to its existing competitive estimator.

The Estimating of the Conditional Density with Application to the Mode Function in Scalar-On-Function Regression Structure: Local Linear Approach with Missing at Random

“…In Rachdi, Laksaci, Demongeot et al (2014), the leading term of the mean quadratic error of the LLE of the conditional density was then explicitly mentioned. Additionally, Zhou and Lin (2016) established the asymptotic normality of the LLE of the regression operator, and recently Almanjahie et al (2022) treated the k Nearest Neighbour kNN LLE of the conditional density in a scalar-On-Function regression structure, for additional research on the LLE in NFDA (Nonparametric Functional Data Analysis), see, Chahad et al (2017); Attouch et al (2017).…”

Wavelet Density and Regression Estimators for Continuous Time Functional Stationary and Ergodic Processes

“…Such tools were extended to classification and discrimination analysis [4] discussed the application of several interesting statistical concepts to the functional data framework, including goodness-of-fit tests, portmanteau tests, and change point problems [5] was interested in analyzing variance for functional data, whereas [6] was more concerned with regression analysis for gaussian processes. Recent studies and surveys on functional data modeling and analysis can be found in [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22].…”

Wavelet Density and Regression Estimators for Functional Stationary and Ergodic Data: Discrete Time

“…The work in [5] focuses on analyzing variance for functional data, whereas that in [6] is more concerned with regression analysis for Gaussian processes. Recent studies and surveys on functional data modeling and analysis can be found in [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22].…”