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Revista Colombiana de Estadística

Print version ISSN 0120-1751

Rev.Colomb.Estad. vol.41 no.2 Bogotá July/Dec. 2018

http://dx.doi.org/10.15446/rce.v41n2.65654 

Artículos originales de investigación

Kernel Function in Local Linear Peters-Belson Regression

Función del núcleo en la regresión lineal local de Peters-Belson

Mohammad Bolbolian Ghalibaf1  a 

1 Department of Statistics, Faculty of Mathematics and Computer Science, Hakim Sabzevari Univercity, Sabzevar, Iran.

Abstract

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.

Key words: Kernel Function; Local Linear Regression; Welch's Approximation

Resumen

Determinar el alcance de una disparidad, si la hubiere, entre grupos de personas, por ejemplo, raza o género, es de interés en muchos campos, incluida la salud pública para el tratamiento médico y la prevención de enfermedades o en casos de discriminación en relación con la igualdad salarial para estimar las disparidades salariales entre los empleados minoritarios y mayoritarios. La regresión de Peters Belson (PB) es una forma de coincidencia estadística, similar en espíritu a la coincidencia de ancho de banda de Bhattacharya que se propone para este propósito. En este trabajo, repasamos el uso de la regresión del PB en casos legales de Bura et al. (2012). Se describen los enfoques paramétricos y no paramétricos de la regresión del PB y demostramos que en la regresión no paramétrica del PB una función de kernel adecuada puede mejorar los resultados, es decir, seleccionando la función de kernel apropiada, podemos reducir el sesgo y la varianza de los estimadores, también aumentan el poder de las pruebas.

Palabras-clave: aproximación de Welch; función kernel; regresión lineal local

Full text available only in PDF format

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a E-mail: m.bolbolian@hsu.ac.ir ; m.bolbolian@gmail.com

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