A Gaussian Approximated Least Squares Estimator for Linear Threshold Models

26 Pages Posted: 24 Jul 2022

Date Written: June 16, 2022

Abstract

Linear threshold models are popularly estimated by the least-squares (LS) method, but the resulted
threshold parameter estimator has a non-standard limiting distribution which makes statistical inference less straightforward. Seo and Linton (2007) introduce a smoothed least-squares (SLS) threshold parameter estimator, which has an asymptotic normality distribution at a cost of a slower convergence rate than the LS estimator. This paper proposes a two-step Gaussian approximated least squares (GALS) estimator and we show that the resulted threshold parameter estimator enjoys the normality limiting distribution, as well as obtains a convergence rate closer to the LS estimator than the SLS estimator. A small Monte Carlo study confirms our theory in finite samples.

Keywords: Estimation, Gaussian Approximation, Linear Threshold Model

JEL Classification: C13, C21, C51

Suggested Citation

Sun, Yiguo, A Gaussian Approximated Least Squares Estimator for Linear Threshold Models (June 16, 2022). Available at SSRN: https://ssrn.com/abstract=4153883 or http://dx.doi.org/10.2139/ssrn.4153883

Yiguo Sun (Contact Author)

University of Guelph ( email )

Guelph, Ontario
Canada

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