On Estimation of Function-on-function Regression Kernels with Brownian Berkson Errors.
Document Type
Lecture
Publication Date
4-11-2024
Abstract
In this paper, we introduce a new methodology to determine an optimal kernel of function-on-function regression in the presence of a stochastic differential equation with Berkson error. We assume that the response variable, unobserved true predictor, the best available observed measure of the true predictor, and the regression kernels are functions of space and time, and the regressor dynamics follow a stochastic differential equation. First, we construct an objective function as a time-dependent Mean Square Error (MSE) and then minimize it with respect to regression coefficients subject to stochastic Berkson error dynamics. A Feynman-type path integral control approach is used to determine a Wick-rotated Schrodinger-type equation that has the complete information of the system. Using first-order conditions for these kernels give us a closed-form solution.
Relational Format
presentation
Recommended Citation
Pramanik, Paramahansa, "On Estimation of Function-on-function Regression Kernels with Brownian Berkson Errors." (2024). Probability & Statistics Seminar. 7.
https://egrove.olemiss.edu/math_statistics/7