k-nearest neighbors prediction and classification for spatial data

We propose a nonparametric predictor and a supervised classification based on the regression function estimate of a spatial real variable using k-nearest neighbors method (k-NN). Under some assumptions, we establish almost complete or sure convergence of the proposed estimates which incorporate a spatial proximity between observations. Numerical results on simulated and real fish data illustrate the behavior of the given predictor and classification method

(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

Robust kernel regression function with uncertain scale parameter for high dimensional ergodic data using k k -nearest neighbor estimation

In this paper, we consider a new method dealing with the problem of estimating the scoring function $\gamma_a$, with a constant $a$, in functional space and an unknown scale parameter under a nonparametric robust regression model. Based on the $k$ Nearest Neighbors ($k$NN) method, the primary objective is to prove the asymptotic normality aspect in the case of a stationary ergodic process of this estimator. We begin by establishing the almost certain convergence of a conditional distribution estimator. Then, we derive the almost certain convergence (with rate) of the conditional median (scale parameter estimator) and the asymptotic normality of the robust regression function, even when the scale parameter is unknown. Finally, the simulation and real-world data results reveal the consistency and superiority of our theoretical analysis in which the performance of the $k$NN estimator is comparable to that of the well-known kernel estimator, and it outperforms a nonparametric series (spline) estimator when there are irrelevant regressors

Binary functional linear models under choice-based sampling

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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