Robust Nonparametric Regression with Simultaneous Scale Curve Estimation

Let $\{X_i, Y_i\}^n_{i=1} \subset \mathbb{R}^d \times \mathbb{R}$ be independent identically distributed random variables. If the conditional distribution $F(y \mid x)$ can be parametrized by $F(y \mid x) = F_0((y - m(x))/\sigma(x))$ with a fixed and known distribution $F_0$ , the regression curve $m(x)$ and scale curve $\sigma(x)$ could be estimated by some parametric method. More generally, we assume that $F$ is unknown and consider nonparametric simultaneous $M$ -type estimates of the unknown functions $m(x)$ and $\sigma(x)$ , using kernel estimators for the conditional distribution function $F(y \mid x)$ . We show pointwise consistency and asymptotic normality of these estimates. The rate of convergence is optimal in the sense of Stone (1980). The asymptotic bias term of this robust estimate turns out to be the same as for the linear Nadaraya-Watson kernel estimate.Let $\{X_i, Y_i\}^n_{i=1} \subset \mathbb{R}^d \times \mathbb{R}$ be independent identically distributed random variables. If the conditional distribution $F(y \mid x)$ can be parametrized by $F(y \mid x) = F_0((y - m(x))/\sigma(x))$ with a fixed and known distribution $F_0$, the regression curve $m(x)$ and scale curve $\sigma(x)$ could be estimated by some parametric method. More generally, we assume that $F$ is unknown and consider nonparametric simultaneous $M$-type estimates of the unknown functions $m(x)$ and $\sigma(x)$, using kernel estimators for the conditional distribution function $F(y \mid x)$. We show pointwise consistency and asymptotic normality of these estimates. The rate of convergence is optimal in the sense of Stone (1980). The asymptotic bias term of this robust estimate turns out to be the same as for the linear Nadaraya-Watson kernel estimate.

摘要来源：OpenAlex 索引摘要（稿件版本未注明）

笔记与分组

分类依据与纠错

Robust Nonparametric Regression with Simultaneous Scale Curve Estimation

代码、数据与补充材料

同时估计尺度曲线的稳健非参数回归

原文摘要

同方向的基础文献

同方向的基础文献