Semi-functional partially linear regression model with responses missing at random
Semi-functional partially linear regression model with responses missing at random
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DOI：
10.1007/s00184-018-0688-6
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发表时间：
2018-10
期刊：
影响因子：
0.7
通讯作者：
N. Ling;Rui Kan;P. Vieu;Shuyu Meng
中科院分区：
文献类型：
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作者：
N. Ling;Rui Kan;P. Vieu;Shuyu Meng
本文重点研究半函数部分线性回归模型，其中随机缺失的标量响应变量可以通过多元随机变量分量的未知线性组合与函数随机变量的未知变换之和来解释，函数随机变量在半度量抽象空间中取值。本文的主要目的是分别构造未知参数的估计量和未知回归算子。然后在一些温和的条件下得到了估计量的一些渐近性质，如非参数分量的几乎确定的收敛率和参数分量的渐近分布。此外，还进行了模拟研究来评估估计器的有限样本性能。最后，对食物脂肪预测的实际数据分析的应用表明了所提出的方法的有用性。
This paper focuses on semi-functional partially linear regression model, where a scalar response variable with missing at random is explained by a sum of an unknown linear combination of the components of multivariate random variables and an unknown transformation of a functional random variable which takes its value in a semi-metric abstract spacewith a semi-metric. The main purpose of this paper is to construct the estimators of unknown parameters and an unknown regression operator respectively. Then some asymptotic properties of the estimators such as almost sure convergence rates of the nonparametric component and asymptotic distribution of the parametric one are obtained under some mild conditions. Furthermore, a simulation study is carried out to evaluate the finite sample performances of the estimators. Finally, an application to real data analysis for food fat predictions shows the usefulness of the proposed methodology.