Compactness of infinite dimensional parameter spaces

Joachim Freyberger and Matthew Masten
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Joachim Freyberger: Institute for Fiscal Studies and University of Bonn

No CWP01/16, CeMMAP working papers from Centre for Microdata Methods and Practice, Institute for Fiscal Studies

Abstract: 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.

Keywords: Nonparametric estimation; sieve estimation; trimming; nonparametric instrumental variables (search for similar items in EconPapers)
JEL-codes: C14 C26 C51 (search for similar items in EconPapers)
Date: 2016-01-03
New Economics Papers: this item is included in nep-ecm and nep-net
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Citations: View citations in EconPapers (5)

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Working Paper: Compactness of infinite dimensional parameter spaces (2016)
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