Abstract

BOLBOLIAN GHALIBAF, Mohammad. Kernel Function in Local Linear Peters-Belson Regression. Rev.Colomb.Estad. [online]. 2018, vol.41, n.2, pp.235-249. ISSN 0120-1751.  https://doi.org/10.15446/rce.v41n2.65654.

Determining the extent of a disparity, if any, between groups of people, for example, race or gender, is of interest in many fields, including public health for medical treatment and prevention of disease or in discrimination cases concerning equal pay to estimate the pay disparities between minority and majority employees. The Peters-Belson (PB) regression is a form of statistical matching, akin in spirit to Bhattacharya's bandwidth matching which is proposed for this purpose. In this paper, we review the use of PB regression in legal cases from Bura, Gastwirth & Hikawa (2012). Parametric and nonparametric approaches to PB regression are described and we show that in nonparametric PB regression a suitable kernel function can improve results, i.e. by selecting the appropriate kernel function, we can reduce bias and variance of estimators, also increase the power of tests.

Keywords : Kernel Function; Local Linear Regression; Welch's Approximation.

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