In applications, other than sample information, some prior information on parameters can be used to improve the estimation efficiency. In the framework of varying-coefficient partially linear models with the number of parametric and nonparametric components diverging, this paper proposes a restricted profile least-squares estimation for the parametric components after the varying coefficients are estimated by basis function approximations. This estimator is shown to be consistent and asymptotically normal under certain regularity conditions. To check the validity of the linear constraints on the parametric components, we construct a profile generalized likelihood ratio test statistic and demonstrate that it follows asymptotically chi-squared distribution under the null and alternative hypotheses. Simulation studies are conducted and the Boston housing data is analyzed to illustrate the proposed method.

中文翻译：

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具有分散数量的半参数变系数部分线性模型的统计推断

在应用中，除了样本信息外，一些关于参数的先验信息可以用来提高估计效率。在参数和非参数分量数量互不相同的变系数部分线性模型的框架下，本文提出了用基函数逼近法估计变化系数后，对参数分量进行限制轮廓最小二乘估计的方法。在某些规律性条件下，该估计量被证明是一致且渐近正态的。为了检查线性约束对参数分量的有效性，我们构造了一个概貌广义似然比检验统计量，并证明了在零假设和替代假设下，它遵循渐近卡方分布。