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A practical guide to compact infinite dimensional parameter spaces

Publication ,  Journal Article
Freyberger, J; Masten, MA
Published in: Econometric Reviews
October 21, 2019

Compactness is a widely used assumption in econometrics. In this article, we gather and review general compactness results for many commonly used parameter spaces in nonparametric estimation, and we provide several new results. 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 illustrate how the choice of norms affects the parameter space, the strength of the conclusions, as well as other regularity conditions in two common settings: nonparametric mean regression and nonparametric instrumental variables estimation.

Duke Scholars

Published In

Econometric Reviews

DOI

EISSN

1532-4168

ISSN

0747-4938

Publication Date

October 21, 2019

Volume

38

Issue

9

Start / End Page

979 / 1006

Related Subject Headings

  • Econometrics
  • 3802 Econometrics
  • 1403 Econometrics
 

Citation

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Chicago
ICMJE
MLA
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Freyberger, J., & Masten, M. A. (2019). A practical guide to compact infinite dimensional parameter spaces. Econometric Reviews, 38(9), 979–1006. https://doi.org/10.1080/07474938.2018.1514025
Freyberger, J., and M. A. Masten. “A practical guide to compact infinite dimensional parameter spaces.” Econometric Reviews 38, no. 9 (October 21, 2019): 979–1006. https://doi.org/10.1080/07474938.2018.1514025.
Freyberger J, Masten MA. A practical guide to compact infinite dimensional parameter spaces. Econometric Reviews. 2019 Oct 21;38(9):979–1006.
Freyberger, J., and M. A. Masten. “A practical guide to compact infinite dimensional parameter spaces.” Econometric Reviews, vol. 38, no. 9, Oct. 2019, pp. 979–1006. Scopus, doi:10.1080/07474938.2018.1514025.
Freyberger J, Masten MA. A practical guide to compact infinite dimensional parameter spaces. Econometric Reviews. 2019 Oct 21;38(9):979–1006.

Published In

Econometric Reviews

DOI

EISSN

1532-4168

ISSN

0747-4938

Publication Date

October 21, 2019

Volume

38

Issue

9

Start / End Page

979 / 1006

Related Subject Headings

  • Econometrics
  • 3802 Econometrics
  • 1403 Econometrics