Adaptive nonparametric instrumental variables estimation: Empirical choice of the regularisation parameter

Arbeitspapier

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.

Object Details

• Language: Englisch

References and Relationships

• Bibliographic citation: Series: cemmap working paper ; No. CWP30/13

Classification and Topics

• Classification: Wirtschaft ; Estimation: General ; Semiparametric and Nonparametric Methods: General ; Single Equation Models; Single Variables: Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions
• Subject: Ill-posed inverse problem ; regularization ; sieve estimation ; series estimation ; nonparametric estimation

Contributors, Places and Time

• Event: Geistige Schöpfung
• (who): Horowitz, Joel
• Event: Veröffentlichung
• (who): Centre for Microdata Methods and Practice (cemmap)
• (where): London
• (when): 2012

Further information

• DOI: doi:10.1920/wp.cem.2013.3013
• Handle: http://hdl.handle.net/10419/79530
• Last update: 10.03.2025, 11:44 AM CET