In this paper, we investigate the asymptotic properties of a nonparametric estimator of the relative error regression given a functional explanatory variable, in the case of a scalar censored response, we use the mean squared relative error as a loss function to construct a nonparametric estimator of the regression operator of these functional censored data. We establish the strong almost complete convergence rate and asymptotic normality of these estimators. A simulation study is performed to illustrate and compare the higher predictive performances of our proposed method to those obtained with standard estimators.

In this paper, we study the semi-functional partial linear regression for spatial data with considering a both parametric and nonparametric modeling. In this case we obtain the asymptotic normality of the parametric component, and probability convergence with rate of the nonparametric component under spatial dependency. Finally, the performance of the parametric and nonparametric estimators, for finite spatial sample sizes, are given by using simulated and real data with comparison to the nonparametric kernel regression (FNR) model by using cross-validation and k nearest neighbor methods.

The problem of predicting continuous scalar outcomes from functional predictors has received high levels of interest in recent years in many fields, especially in the food industry. The k-nearest neighbor (k-NN) method of Near-Infrared Reflectance (NIR) analysis is practical, relatively easy to implement, and becoming one of the most popular methods for conducting food quality based on NIR data. The k-NN is often named k nearest neighbor classifier when it is used for classifying categorical variables, while it is called k-nearest neighbor regression when it is applied for predicting noncategorical variables. The objective of this paper is to use the functional Near-Infrared Reflectance (NIR) spectroscopy approach to predict some chemical components with some modern statistical models based on the kernel and k-Nearest Neighbour procedures. In this paper, three NIR spectroscopy datasets are used as examples, namely Cookie dough, sugar, and tecator data. Specifically, we propose three models for this kind of data which are Functional Nonparametric Regression, Functional Robust Regression, and Functional Relative Error Regression, with both kernel and k-NN approaches to compare between them. The experimental result shows the higher efficiency of k-NN predictor over the kernel predictor. The predictive power of the k-NN method was compared with that of the kernel method, and several real data sets were used to determine the predictive power of both methods.