We propose a kernel density based estimation by constructing a nonparametric kernel version of the maximum profile likelihood estimator for partial linear multivariate responses regression models. The method proposed in this article makes use of multivariate kernel smoothing nonparametric techniques to estimate the unknown multivariate density function. For the hypothesis testing of parametric components, restricted estimators under the null hypothesis and test statistics are proposed. The asymptotic properties for the estimators and test statistics are established. We illustrate our proposals through simulations and an analysis of the energy efficiency data. Our analysis provides strong evidence that the proposed kernel density based estimator is superior than the profile least squares estimator, particularly for multimodal or heavy-tailed distributions of the model errors.

通过为部分线性多元响应回归模型构建最大轮廓似然估计器的非参数内核版本，我们提出了基于内核密度的估计。本文提出的方法利用多元核平滑非参数技术来估计未知的多元密度函数。对于参数分量的假设检验，提出了原假设和检验统计量下的受限估计量。建立估计量和检验统计量的渐近性质。我们通过模拟和对能效数据的分析来说明我们的建议。我们的分析提供了有力的证据，表明所提出的基于核密度的估计量优于轮廓最小二乘估计量，