A1368
Title: Nonparametric bootstrap solution to the multivariate inverse regression problem
Authors: Angel Mae Pailden - University of the Philippines Diliman (Philippines) [presenting]
Michael Daniel Lucagbo - University of the Philippines Diliman (Philippines)
Abstract: Multivariate inverse regression, also known as the multivariate calibration problem, involves estimating unknown covariate values using information from the response vector. The problem of interest concerns constructing a confidence region for an unknown covariate parameter vector when both the coefficient matrix and error covariance are unknown. This topic has been studied in relevant literature, with most existing methods relying on distributional results that are tractable only under strong parametric assumptions. However, when these assumptions are not met, conventional methods lose reliability. A rectangular region construction method using a nonparametric bootstrap approach to the multivariate controlled calibration problem is proposed. The bootstrap algorithm is demonstrated through numerical simulations to be effective in maintaining nominal coverage while yielding interpretable rectangular regions. The method is further extended to nonlinear models involving polynomial covariates. Applications using wheat quality data and paint finish data illustrate the approach.
