Nonparametric M-regression with Scale Parameter For Functional Dependent Data

In this paper, we study the equivariant nonparametric robust regression estimation relationship between a functional dependent random covariable and a scalar response. We consider a new robust regression estimator when the scale parameter is unknown. The consistency result of the proposed estimator is studied, namely the uniform almost complete convergence (with rate). Thus, suitable topological considerations are needed, implying changes in the convergence rates, which are quantified by entropy considerations. The benefits of considering robust estimators are illustrated on two real data sets where the robust fit reveals the presence of influential outliers

(R1899) Asymptotic Normality of the Conditional Hazard Function in the Local Linear Estimation Under Functional Mixing Data

In this study, we are interested in using the local linear technique to estimate the conditional hazard function for functional dependent data where the scalar response is conditioned by a functional random variable. The asymptotic normality of this constructed estimator is demonstrated under some extreme conditions. Our estimator’s performance is demonstrated through simulations

(R1953) M-Regression Estimation with the k Nearest Neighbors Smoothing under Quasi-associated Data in Functional Statistics

The main goal of this paper is to study the non parametric M-estimation under quasi-associated sequence with the k Nearest Neighbor’s method shortly (kNN). We construct an estimator of this nonparametric function and we study its asymptotic properties. Furthermore, a comparison study based on simulated data is also provided to illustrate the highly sensitive of the kNN approach to the presence of even a small proportion of outliers in the data

Asymptotic Normality of Nonparametric Kernel Regression Estimation for Missing at Random Functional Spatial Data

This study investigates the estimation of the regression function using the kernel method in the presence of missing at random responses, assuming spatial dependence, and complete observation of the functional regressor. We construct the asymptotic properties of the established estimator and derive the probability convergence (with rates) as well as the asymptotic normality of the estimator under certain weak conditions. Simulation studies are then presented to examine and show the performance of our proposed estimator. This is followed by examining a real data set to illustrate the suggested estimator’s efficacy and demonstrate its superiority. The results show that the proposed estimator outperforms existing estimators as the number of missing at random data increases