Limit theory for locally flat functional coefficient regression
Limit theory for locally flat functional coefficient regression
Functional coefficient (FC) regressions allow for systematic flexibility in the responsiveness of a dependent variable to movements in the regressors, making them attractive in applications where marginal effects may depend on covariates. Such models are commonly estimated by local kernel regression methods. This paper explores situations where responsiveness to covariates is locally flat or fixed. The paper develops new asymptotics that take account of shape characteristics of the function in the locality of the point of estimation. Both stationary and integrated regressor cases are examined. The limit theory of FC kernel regression is shown to depend intimately on functional shape in ways that affect rates of convergence, optimal bandwidth selection, estimation, and inference. In FC cointegrating regression, flat behavior materially changes the limit distribution by introducing the shape characteristics of the function into the limiting distribution through variance as well as centering. In the boundary case where the number of zero derivatives tends to infinity, near parametric rates of convergence apply in stationary and nonstationary cases. Implications for inference are discussed and a feasible pre-test inference procedure is proposed that takes unknown potential flatness into consideration and provides a practical approach to inference.
1-50
Phillips, Peter C. B.
f67573a4-fc30-484c-ad74-4bbc797d7243
Wang, Ying
52de6d30-ee62-4a76-a8b6-576dc578f3cd
14 July 2022
Phillips, Peter C. B.
f67573a4-fc30-484c-ad74-4bbc797d7243
Wang, Ying
52de6d30-ee62-4a76-a8b6-576dc578f3cd
Phillips, Peter C. B. and Wang, Ying
(2022)
Limit theory for locally flat functional coefficient regression.
Econometric Theory, .
(doi:10.1017/S0266466622000287).
Abstract
Functional coefficient (FC) regressions allow for systematic flexibility in the responsiveness of a dependent variable to movements in the regressors, making them attractive in applications where marginal effects may depend on covariates. Such models are commonly estimated by local kernel regression methods. This paper explores situations where responsiveness to covariates is locally flat or fixed. The paper develops new asymptotics that take account of shape characteristics of the function in the locality of the point of estimation. Both stationary and integrated regressor cases are examined. The limit theory of FC kernel regression is shown to depend intimately on functional shape in ways that affect rates of convergence, optimal bandwidth selection, estimation, and inference. In FC cointegrating regression, flat behavior materially changes the limit distribution by introducing the shape characteristics of the function into the limiting distribution through variance as well as centering. In the boundary case where the number of zero derivatives tends to infinity, near parametric rates of convergence apply in stationary and nonstationary cases. Implications for inference are discussed and a feasible pre-test inference procedure is proposed that takes unknown potential flatness into consideration and provides a practical approach to inference.
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Flat_FC_limit_2022_May_19_ying
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limit-theory-for-locally-flat-functional-coefficient-regression
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Accepted/In Press date: 20 May 2022
e-pub ahead of print date: 14 July 2022
Published date: 14 July 2022
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Funding Information:
Our thanks go to the Co-Editor, Liangjun Su, and two referees for most helpful comments on the earlier versions of this paper. Phillips acknowledges research support from the NSF under Grant No. SES 18-50860 at Yale University and a Kelly Fellowship at the University of Auckland. Wang acknowledges support from the National Natural Science Foundation of China (Grant No. 72103197).
Publisher Copyright:
© The Author(s), 2022. Published by Cambridge University Press.
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Local EPrints ID: 472158
URI: http://eprints.soton.ac.uk/id/eprint/472158
ISSN: 0266-4666
PURE UUID: f9e72e2f-ccf0-406d-ad29-4bd105326d21
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Date deposited: 28 Nov 2022 17:58
Last modified: 16 Mar 2024 21:35
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Ying Wang
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