Compactness of infinite dimensional parameter spaces

Arbeitspapier

We provide general compactness results for many commonly used parameter spaces in nonparametric estimation. We consider three kinds of functions: (1) functions with bounded domains which satisfy standard norm bounds, (2) functions with bounded domains which do not satisfy standard norm bounds, and (3) functions with unbounded domains. In all three cases we provide two kinds of results, compact embedding and closedness, which together allow one to show that parameter spaces defined by a ║·║s-norm bound are compact under a norm ║·║c. We apply these results to nonparametric mean regression and nonparametric instrumental variables estimation.

Object Details

• Language: Englisch

References and Relationships

• Bibliographic citation: Series: cemmap working paper ; No. CWP01/16

Classification and Topics

• Classification: Wirtschaft ; Semiparametric and Nonparametric Methods: General ; Single Equation Models: Single Variables: Instrumental Variables (IV) Estimation ; Model Construction and Estimation
• Subject: Nonparametric Estimation ; Sieve Estimation ; Trimming ; Nonparametric Instrumental Variables

Contributors, Places and Time

• Event: Geistige Schöpfung
• (who): Freyberger, Joachim ; Masten, Matthew
• Event: Veröffentlichung
• (who): Centre for Microdata Methods and Practice (cemmap)
• (where): London
• (when): 2015

Further information

• DOI: doi:10.1920/wp.cem.2016.0116
• Handle: http://hdl.handle.net/10419/130087
• Last update: 10.03.2025, 11:43 AM CET