2022 / June Volume 17 No.2
High dimensional statistics: Quadratic error in the local linear estimation of the relative regression
| Published Date |
2022 / June
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|---|---|
| Title | High dimensional statistics: Quadratic error in the local linear estimation of the relative regression |
| Author | |
| Keyword | |
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| Pagination | 235-248 |
| 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.
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| DOI | |
| AMS Subject Classification |
62G05, 62G08, 62G20, 62G35, 62H12
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| Received |
2022-01-21
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