Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/79530
Authors: 
Horowitz, Joel
Year of Publication: 
2012
Series/Report no.: 
cemmap working paper, Centre for Microdata Methods and Practice CWP30/13
Abstract: 
In nonparametric instrumental variables estimation, the mapping that identifies the function of interest, g say, is discontinuous and must be regularised (that is, modified) to make consistent estimation possible. The amount of modification is contolled by a regularisation parameter. The optimal value of this parameter depends on unknown population characteristics and cannot be calculated in applications. Theoretically justified methods for choosing the regularisatoin parameter empirically in applications are not yet available. This paper presents such a method for use in series estimation, where the regularisation parameter is the number of terms in a series approximation to g. The method does not required knowledge of the smoothness of g or of other unknown functions. It adapts to their unknown smoothness. The estimator of g based on the empirically selected regularisation parameter converges in probabillity at a rate that is at least as fast as the asymptotically optimal rate multiplied by (logn)1/2, where n is the sample size. The asymptotic integrated mean-square error (AIMSE) of the estimator is within a specified factor of the optimal AIMSE.
Subjects: 
Ill-posed inverse problem
regularization
sieve estimation
series estimation
nonparametric estimation
JEL: 
C13
C14
C21
Persistent Identifier of the first edition: 
Document Type: 
Working Paper

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