Simultaneous Inference of the Partially Linear Model with a Multivariate Unknown Function - Kun Ho Kim; Shih-Kang Chao; Wolfgang Karl Härdle (Humboldt-Universität zu Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series", 2020)
In this paper, we conduct simultaneous inference of the non-parametric part of a partially linear model when the non-parametric component is a multivariate unknown function. Based on semi-parametric estimates of the model, we construct a simultaneous confidence region of the multivariate function for simultaneous inference. The developed methodology is applied to perform simultaneous inference for the U.S. gasoline demand where the income and price variables are contaminated by Berkson errors. The empirical results strongly suggest that the linearity of the U.S. gasoline demand is rejected. The results are also used to propose an alternative form for the demand.
Keywords: C12; C13; C14; 330; Simultaneous inference; Multivariate function; Simultaneous confidence region; Berkson error; Regression calibration