Asymptotic results of semi-functional partial linear regression estimate under functional spatial dependency

Nonparametric Partial Linear Estimation for Spatial Functional Data with Missing At-Random

“…We note that these results obtained extend those which are established in the case of complete data (see [20]).…”

“…Furthermore, only a few research works have paid attention to estimation in the semi-functional partial linear regression model for spatially dependent observations. We cite the work of [19] on the autoregressive semi-functional linear regression (SAR) model, which proposed an estimator based on the method of quasi-maximum likelihood and local linear estimation while [20] obtained the asymptotic normality of the parametric component as well as the convergence in probability with the rate of the nonparametric component. The complete analysis of the data is the subject of all the works listed.…”

Functional Nonparametric Predictions in Food Industry Using Near-Infrared Spectroscopy Measurement

“…This work extends the multidimensional framework by setting the response variable in a dimensional space. The comparison of the generated estimator when there are outlier's outputs is an important natural issue that we would be treating and that has not been considered in this work (see, for example, [17] and [26]). This research combines contemporary chemistry techniques with recent developments in mathematical statistics to produce effective prediction processes that use the entire curves as regressors.…”

“…Reference [15] suggested a knearest-neighbors (k-NN) approach and obtained the asymptotic performances of k-NN estimators, whereas [16] investigated a semi-functional partly linear regression model with random responses. Reference [17] investigated semi-functional partial linear regression for spatial data and obtained asymptotic normality of the parametric component as well as probability convergence with the rate of the nonparametric component.…”

A Literature Review of Semi-functional Partial Linear Regression Models

“… Bayesian: The Bayesian estimation methods are present in some papers ,but we only mention these two papers in this part: the Bayesian bandwidth estimation and semi-metric selection for a functional partial linear model with unknown error density [36,37].  Spatial: The spatial variability is considered in many research articles such as The partial functional linear spatial regression autoregressive model with spatial dependence responses [38], with two-stage estimator based on quasi-maximum likelihood estimation (QMLE) method and local linear regression method [39], studying the asymptotic normality of the parametric component, and probability convergence with the rate of the nonparametric component [40], B-spline approximation for slope function and residualbased approach for pointwise confidence-intervals [41], the robust spatial autoregressive model with t-distribution error terms with an expectationmaximization algorithm [42].  Robust: Existing outliers in the data or violations from distributional assumptions yield to the robust methods such as the sieve M-estimator for semi-functional linear model [43], with polynomial splines to approximate the slope parameter and resistance to heavy-tailed errors or outliers in the response [44], different estimators such as M-estimators with bi-square function, GM-estimator with Huber function, LMS-estimator and LTS-estimators [45], estimation based on exponential squared loss and FPCA [46], estimation based on the class of scale mixtures of normal (SMN) distributions for measurement errors and Bayesian framework with MCMC algorithm [47], Robust MM-estimators with B-Spline approximation [48], with modal regression [49] and a modified Huber's function with tail function with a data-driven procedure for selecting the tuning parameters [50].…”