Published

2018-07-01

Kernel Function in Local Linear Peters-Belson Regression

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

DOI:

https://doi.org/10.15446/rce.v41n2.65654

Keywords:

Kernel Function, Local Linear Peters-Belson Regression, Majority Group, Minority Group, Welch's Approximation. (en)
Aproximación de Welch, función kernel, regresión lineal local (es)

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Authors

  • Mohammad Bolbolian Ghalibaf Department of Statistics‎,‎ ‎‎Faculty of Mathematical Sciences and Computer‎, Hakim Sabzevari‎ University,‎ Sabzevar‎‎‎, ‎Iran
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. An observed difference in the mean outcome between a majority/advantaged group (AG) and minority/disadvantaged group (DG) can be due to differences in the distribution of relevant covariates. The Peters Belson (PB) method fits a regression model with covariates to the AG to predict, for each DG member, their outcome measure as if they had been from the AG. The difference between the mean predicted and the mean observed outcomes of DG members is the (unexplained) disparity of interest. PB regression is a form of statistical matching, akin in spirit to Bhattacharya's band-width matching. In this paper we review the use of PB regression in legal cases from Hikawa et al. (2010b) Parametric and nonparametric approaches to PB regression are described and we show that in nonparametric PB regression choose a kernel function can be better resulted, i.e. by selecting the appropriate kernel function we can reduce bias and variance of estimators, also increase power of test.

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.

References

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How to Cite

APA

Bolbolian Ghalibaf, M. (2018). Kernel Function in Local Linear Peters-Belson Regression. Revista Colombiana de Estadística, 41(2), 235–249. https://doi.org/10.15446/rce.v41n2.65654

ACM

[1]
Bolbolian Ghalibaf, M. 2018. Kernel Function in Local Linear Peters-Belson Regression. Revista Colombiana de Estadística. 41, 2 (Jul. 2018), 235–249. DOI:https://doi.org/10.15446/rce.v41n2.65654.

ACS

(1)
Bolbolian Ghalibaf, M. Kernel Function in Local Linear Peters-Belson Regression. Rev. colomb. estad. 2018, 41, 235-249.

ABNT

BOLBOLIAN GHALIBAF, M. Kernel Function in Local Linear Peters-Belson Regression. Revista Colombiana de Estadística, [S. l.], v. 41, n. 2, p. 235–249, 2018. DOI: 10.15446/rce.v41n2.65654. Disponível em: https://revistas.unal.edu.co/index.php/estad/article/view/65654. Acesso em: 28 mar. 2025.

Chicago

Bolbolian Ghalibaf, Mohammad. 2018. “Kernel Function in Local Linear Peters-Belson Regression”. Revista Colombiana De Estadística 41 (2):235-49. https://doi.org/10.15446/rce.v41n2.65654.

Harvard

Bolbolian Ghalibaf, M. (2018) “Kernel Function in Local Linear Peters-Belson Regression”, Revista Colombiana de Estadística, 41(2), pp. 235–249. doi: 10.15446/rce.v41n2.65654.

IEEE

[1]
M. Bolbolian Ghalibaf, “Kernel Function in Local Linear Peters-Belson Regression”, Rev. colomb. estad., vol. 41, no. 2, pp. 235–249, Jul. 2018.

MLA

Bolbolian Ghalibaf, M. “Kernel Function in Local Linear Peters-Belson Regression”. Revista Colombiana de Estadística, vol. 41, no. 2, July 2018, pp. 235-49, doi:10.15446/rce.v41n2.65654.

Turabian

Bolbolian Ghalibaf, Mohammad. “Kernel Function in Local Linear Peters-Belson Regression”. Revista Colombiana de Estadística 41, no. 2 (July 1, 2018): 235–249. Accessed March 28, 2025. https://revistas.unal.edu.co/index.php/estad/article/view/65654.

Vancouver

1.
Bolbolian Ghalibaf M. Kernel Function in Local Linear Peters-Belson Regression. Rev. colomb. estad. [Internet]. 2018 Jul. 1 [cited 2025 Mar. 28];41(2):235-49. Available from: https://revistas.unal.edu.co/index.php/estad/article/view/65654

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