Nonparametric instrumental regression with non-convex constraints

Grasmair, M, Scherzer, O and Vanhems, Anne (2013) Nonparametric instrumental regression with non-convex constraints. Inverse problems, 29 (3).

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This paper considers the nonparametric regression model with an additive error that is dependent on the explanatory variables. As is common in empirical studies in epidemiology and economics, it also supposes that valid instrumental variables are observed. A classical example in microeconomics considers the consumer demand function as a function of the price of goods and the income, both variables often considered as endogenous. In this framework, the economic theory also imposes shape restrictions on the demand function, such as integrability conditions. Motivated by this illustration in microeconomics, we study an estimator of a nonparametric constrained regression function using instrumental variables by means of Tikhonov regularization. We derive rates of convergence for the regularized model both in a deterministic and stochastic setting under the assumption that the true regression function satisfies a projected source condition including, because of the non-convexity of the imposed constraints, an additional smallness condition.

Item Type: Article
Language: English
Date: March 2013
Refereed: Yes
Divisions: TSE-R (Toulouse)
Site: UT1
Date Deposited: 09 Jul 2014 17:33
Last Modified: 07 Mar 2018 13:22

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