Humboldt-Universität zu Berlin - High Dimensional Nonstationary Time Series

IRTG1792DP2020 008

Simultaneous Inference of the Partially Linear Model with a Multivariate Unknown

Kun Ho Kim
Shih-Kang Chao
Wolfgang K. Härdle

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.

Simultaneous inference, Multivariate function, Simultaneous confidence region,
Berkson error, Regression calibration

JEL Classification:
C12, C13, C14