Nonparametric relative error estimation of the regression function for censored data
Let $ (T_i)_i$ be a sequence of independent identically distributed (i.i.d.) random variables (r.v.) of interest distributed as $ T$ and $(X_i)_i$ be a corresponding vector of covariates taking values on $ \mathbb{R}^d$. In censorship models the r.v. $T$ is subject to random censoring by another r.v...
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| Main Authors | , , |
|---|---|
| Format | Journal Article |
| Language | English |
| Published |
28.01.2019
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| Subjects | |
| Online Access | Get full text |
| DOI | 10.48550/arxiv.1901.09555 |
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| Summary: | Let $ (T_i)_i$ be a sequence of independent identically distributed (i.i.d.)
random variables (r.v.) of interest distributed as $ T$ and $(X_i)_i$ be a
corresponding vector of covariates taking values on $ \mathbb{R}^d$. In
censorship models the r.v. $T$ is subject to random censoring by another r.v.
$C$. In this paper we built a new kernel estimator based on the so-called
synthetic data of the mean squared relative error for the regression function.
We establish the uniform almost sure convergence with rate over a compact set
and its asymptotic normality. The asymptotic variance is explicitly given and
as product we give a confidence bands. A simulation study has been conducted to
comfort our theoretical results |
|---|---|
| DOI: | 10.48550/arxiv.1901.09555 |