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High dimensional statistics: Quadratic error in the local linear estimation of the relative regression
by Oussama Bouanani   Mustapha Rachdi   Saâdia Rahmani

Vol. 17 No. 2 (2022) P.235~P.248
 DOI: https://doi.org/10.21915/BIMAS.2022206 10.21915/BIMAS.2022206

ABSTRACT

In this paper, we use the mean squared relative error as a loss function to construct a local linear estimator of the regression operator. More precisely, we consider n pairs of independent random variables ($X_i$, $Y_i$) for $i$ = 1, . . . , $n$ that we assume drawn from the pair ($X$, $Y$), which is valued in ($\mathfrak{F}$, $\mathbb{R}$), where $\mathfrak{F}$ is a semi-metric space equipped with the semi-metric $d$. Under some standard assumptions, we give the convergence rate in mean square of the constructed estimator. The usefulness of the estimator is highlighted through the exact expression involved in the leading terms of the quadratic error. Notice that this method is useful in analyzing data with positive responses, such as life times.

KEYWORDS
Functional data, local linear estimator, relative error, nonparametric estimation, mean square quadratic error.

MATHEMATICAL SUBJECT CLASSIFICATION 2010
Primary: 62G05, 62G08, 62G20, 62G35, 62H12

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