Kernel density estimation for partial linear multivariate responses models

Abstract 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.