Partially Linear Models
Partially Linear Models
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DOI：
10.1007/978-3-540-32691-5_5
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发表时间：
2000-10
期刊：
影响因子：
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通讯作者：
W. Härdle;Hua Liang;Jiti Gao
中科院分区：
文献类型：
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作者：
W. Härdle;Hua Liang;Jiti Gao
部分线性模型（PLM）是一种响应与部分协变量呈线性关系而与其他协变量呈非参数关系的回归模型。plm推广了标准线性回归技术，是可加模型的特殊情况。本章涵盖了基本结果，并解释了plm如何在生物识别实践中应用。更具体地说，我们主要关注线性参数的最小二乘估计，而非参数部分则通过核回归，样条近似，分段多项式和局部多项式技术进行估计。当模型为异方差时，用加权最小二乘估计近似方差函数。许多例子说明了在实践中的实现。
Partially linear models (PLM) are regression models in which the response depends on some covariates linearly but on other covariates nonparametrically. PLMs generalize standard linear regression techniques and are special cases of additive models. This chapter covers the basic results and explains how PLMs are applied in the biometric practice. More specifically, we are mainly concerned with least squares estimators of the linear parameter while the nonparametric part is estimated by eg kernel regression, spline approximation, piecewise polynomial and local polynomial techniques. When the model is heteroscedastic, the variance functions are approximated by weighted least squares estimators. Numerous examples illustrate the implementation in practice.