We consider testing for correct specification of a nonparametric instrumental variable regression. In this ill-posed inverse problem setting, the test statistic is based on the empirical minimum distance criterion corresponding to the conditional moment restriction evaluated with a Tikhonov...

In this paper we are concerned with shape restricted estimation in inverse regression problems with convolution-type operator. We use increasing rearrangements to compute increasingand convex estimates from an (in principle arbitrary) unconstrained estimate of the unknown regression function. An...

We study the asymptotic distribution of Tikhonov Regularized estimation of quantile structural effects implied by a nonseparable model. The nonparametric instrumental variable estimator is based on a minimum distance principle. We show that the minimum distance problem without regularization is...

This paper proposes a new Bayesian approach for estimating, nonparametrically, parameters in econometric models that are characterized as the solution of a linear inverse problem. By using a Gaussian process prior distribution we propose the posterior mean as an estimator and prove consistency,...

We propose an iterative algorithm for the minimization of a ℓ <Subscript>1</Subscript>-norm penalized least squares functional, under additional linear constraints. The algorithm is fully explicit: it uses only matrix multiplications with the three matrices present in the problem (in the linear constraint, in the...</subscript>

The purpose of this paper is to initiate a discussion on the incorrect nature of our economic–econometric models and methods, and to make a plea for information theoretic recovery methods consistent with the data that we must use and with the questions that we need to ask.

Abstract We are interested in the problem of estimating a regression function φ observed with a correlated noise Y  =  φ ( X )+ U . Contrary to the usual regression model, U is not centered conditionaly on X but rather on an observed variable W . Hence this model turns to be a difficult...