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Last edited on
Jun 20, 2025 by JJ
.
Thesis:
Master in Mathematics

Author:
Lorenz Kiesel

Title:
Nonparametric Bayesian instrumental regression

Supervisors:
Jan JOHANNES

Abstract:
This thesis develops a Quasi-Bayesian nonparametric approach for estimating the structural relationship in instrumental IV regression models, formulated as an inverse problem. Building on tools from the theory of Bayesian inverse problems, we demonstrate that the classical Bayesian approach leads to inconsistent estimates in the frequentist sense. We interpret this inconsistency as a manifestation of the ill-posedness inherent in the inverse problem. To address this issue, we regularize the posterior distribution using a Tikhonov-regularization scheme, motivated by a penalized projection argument. This regularization justifies the Quasi-Bayesian terminology. We show that the resulting regularized posterior distribution is consistent, and the corresponding posterior mean estimator converges to the true structural function in the frequentist sense. Our analysis highlights the critical interaction between prior specification, regularization, and convergence rates in nonparametric IV regression models.

Reference:
J.-P. Florens and A. Simoni. Nonparametric estimation of an instrumental regression: a quasi-bayesian approach based on regularized posterior, Toulouse School of Economics, 2010.