Nonparametric Relative Error Estimation via Functional Regressor by the k Nearest Neighbors Smoothing Under Truncation Random Data

The relation between a functional random covariate and a scalar answer due to left truncation by a different random variable is evaluated in this study with the kNN method. In particular, in order to produce a nonparametric kNN regression operator of these functional truncated data as a loss function, we should use mean squared relative error. In number of neighbors, we establish an estimator and assess the uniform consistency performance with the convergence rate. Then, for different levels of computational truncated data, a simulation analysis was carried out on finite-sized samples to show the feasibility of our estimation procedure and to highlight its superiority to traditional kernel estimation

(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

Szacowanie gęstości warunkowej z wykorzystaniem modelu w strukturze regresji skalarnej na funkcji: lokalne podejście liniowe z losowym brakiem

The aim of this research was to study a nonparametric estimator of the density and mode function of a scalar response variable given a functional variable, when the observations are i.i.d. This proposed estimator is given by combining Missing At Random (MAR) with the local linear approach. Finally, a comparison study based on simulated data is also provided to illustrate the finite sample performances and the usefulness of the local linear approach with MAR to the presence of even a small proportion of outliers in the data.Celem analizy było zbadanie nieparametrycznego estymatora funkcji gęstości i trybu skalarnej zmiennej odpowiedzi na zmienną funkcyjną, gdy obserwacje są i.i.d. Ten proponowany estymator jest tworzony przez połączenie metody Missing At Random (MAR) z lokalnym podejściem liniowym. Na koniec zapewniono również badanie porównawcze oparte na symulowanych danych, aby zilustrować wydajność skończonej próbki i przydatność lokalnego podejścia liniowego z MAR do obecności nawet niewielkiej części wartości odstających w danych

Warunkowa funkcja rozkładu z funkcjonalną zmienną wyjaśniającą: przypadek danych przestrzennych i metody k-najbliższego sąsiada

In this paper the author introduced a new conditional distribution function estimator, in short (cdf), when the co-variables are functional in nature. This estimator is a mix of both procedures the k Nearest Neighbour method and the spatial functional estimation.W artykule opisano nowy estymator funkcji rozkładu warunkowego (CDF) używany, gdy współzmienne mają charakter funkcjonalny. Ten estymator jest połączeniem obu procedur: k-najbliższego sąsiada i przestrzennej estymacji funkcjonalnej