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Strong consistency rates for the estimators in a heteroscedastic EV model with missing responses
Journal of Inequalities and Applications ( IF 1.6 ) Pub Date : 2020-05-24 , DOI: 10.1186/s13660-020-02411-y Jing-Jing Zhang , Yun-Peng Xiao
Journal of Inequalities and Applications ( IF 1.6 ) Pub Date : 2020-05-24 , DOI: 10.1186/s13660-020-02411-y Jing-Jing Zhang , Yun-Peng Xiao
This article is concerned with the semi-parametric error-in-variables (EV) model with missing responses: $y_{i}= \xi _{i}\beta +g(t_{i})+\epsilon _{i}$, $x_{i}= \xi _{i}+\mu _{i}$, where $\epsilon _{i}=\sigma _{i}e_{i}$ is heteroscedastic, $f(u_{i})=\sigma ^{2}_{i}$, $y_{i}$ are the response variables missing at random, the design points $(\xi _{i},t_{i},u_{i})$ are known and non-random, β is an unknown parameter, $g(\cdot )$ and $f(\cdot )$ are functions defined on closed interval $[0,1]$, and the $\xi _{i}$ are the potential variables observed with measurement errors $\mu _{i}$, $e_{i}$ are random errors. Under appropriate conditions, we study the strong consistent rates for the estimators of β, $g(\cdot )$ and $f(\cdot )$. Finite sample behavior of the estimators is investigated via simulations.
中文翻译:
带有缺失响应的异方差EV模型中估计的强一致性率
本文关注的是缺少响应的半参数变量误差(EV)模型:$ y_ {i} = \ xi _ {i} \ beta + g(t_ {i})+ \ epsilon _ {i } $,$ x_ {i} = \ xi _ {i} + \ mu _ {i} $,其中$ \ epsilon _ {i} = \ sigma _ {i} e_ {i} $是异方差的,$ f( u_ {i})= \ sigma ^ {2} _ {i} $,$ y_ {i} $是随机丢失的响应变量,设计点$(\ xi _ {i},t_ {i},u_ {i})$是已知的并且是非随机的,β是未知参数,$ g(\ cdot)$和$ f(\ cdot)$是在闭区间$ [0,1] $上定义的函数,而$ \ xi _ {i} $是观察到的具有测量误差的潜在变量$ \ mu _ {i} $,$ e_ {i} $是随机误差。在适当的条件下,我们研究β,$ g(\ cdot)$和$ f(\ cdot)$的估计的强一致率。通过仿真研究估计器的有限样本行为。
更新日期:2020-05-24
中文翻译:
带有缺失响应的异方差EV模型中估计的强一致性率
本文关注的是缺少响应的半参数变量误差(EV)模型:$ y_ {i} = \ xi _ {i} \ beta + g(t_ {i})+ \ epsilon _ {i } $,$ x_ {i} = \ xi _ {i} + \ mu _ {i} $,其中$ \ epsilon _ {i} = \ sigma _ {i} e_ {i} $是异方差的,$ f( u_ {i})= \ sigma ^ {2} _ {i} $,$ y_ {i} $是随机丢失的响应变量,设计点$(\ xi _ {i},t_ {i},u_ {i})$是已知的并且是非随机的,β是未知参数,$ g(\ cdot)$和$ f(\ cdot)$是在闭区间$ [0,1] $上定义的函数,而$ \ xi _ {i} $是观察到的具有测量误差的潜在变量$ \ mu _ {i} $,$ e_ {i} $是随机误差。在适当的条件下,我们研究β,$ g(\ cdot)$和$ f(\ cdot)$的估计的强一致率。通过仿真研究估计器的有限样本行为。