Kernel Function in Local Linear Peters-Belson Regression

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 minorit...

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Autores:
Bolbolian Ghalibaf, Mohammad
Tipo de recurso:
Article of journal
Fecha de publicación:
2018
Institución:
Universidad Nacional de Colombia
Repositorio:
Universidad Nacional de Colombia
Idioma:
spa
OAI Identifier:
oai:repositorio.unal.edu.co:unal/66486
Acceso en línea:
https://repositorio.unal.edu.co/handle/unal/66486
http://bdigital.unal.edu.co/67514/
Palabra clave:
51 Matemáticas / Mathematics
31 Colecciones de estadística general / Statistics
Kernel Function
Local Linear Peters-Belson Regression
Majority Group
Minority Group
Welch's Approximation.
Aproximación de Welch
función kernel
regresión lineal local
Rights
openAccess
License
Atribución-NoComercial 4.0 Internacional
id UNACIONAL2_6a168656611b5893f280442f1891f06d
oai_identifier_str oai:repositorio.unal.edu.co:unal/66486
network_acronym_str UNACIONAL2
network_name_str Universidad Nacional de Colombia
repository_id_str
dc.title.spa.fl_str_mv Kernel Function in Local Linear Peters-Belson Regression
title Kernel Function in Local Linear Peters-Belson Regression
spellingShingle Kernel Function in Local Linear Peters-Belson Regression
51 Matemáticas / Mathematics
31 Colecciones de estadística general / Statistics
Kernel Function
Local Linear Peters-Belson Regression
Majority Group
Minority Group
Welch's Approximation.
Aproximación de Welch
función kernel
regresión lineal local
title_short Kernel Function in Local Linear Peters-Belson Regression
title_full Kernel Function in Local Linear Peters-Belson Regression
title_fullStr Kernel Function in Local Linear Peters-Belson Regression
title_full_unstemmed Kernel Function in Local Linear Peters-Belson Regression
title_sort Kernel Function in Local Linear Peters-Belson Regression
dc.creator.fl_str_mv Bolbolian Ghalibaf, Mohammad
dc.contributor.author.spa.fl_str_mv Bolbolian Ghalibaf, Mohammad
dc.subject.ddc.spa.fl_str_mv 51 Matemáticas / Mathematics
31 Colecciones de estadística general / Statistics
topic 51 Matemáticas / Mathematics
31 Colecciones de estadística general / Statistics
Kernel Function
Local Linear Peters-Belson Regression
Majority Group
Minority Group
Welch's Approximation.
Aproximación de Welch
función kernel
regresión lineal local
dc.subject.proposal.spa.fl_str_mv Kernel Function
Local Linear Peters-Belson Regression
Majority Group
Minority Group
Welch's Approximation.
Aproximación de Welch
función kernel
regresión lineal local
description 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.
publishDate 2018
dc.date.issued.spa.fl_str_mv 2018-07-01
dc.date.accessioned.spa.fl_str_mv 2019-07-03T02:13:16Z
dc.date.available.spa.fl_str_mv 2019-07-03T02:13:16Z
dc.type.spa.fl_str_mv Artículo de revista
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dc.identifier.issn.spa.fl_str_mv ISSN: 2389-8976
dc.identifier.uri.none.fl_str_mv https://repositorio.unal.edu.co/handle/unal/66486
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identifier_str_mv ISSN: 2389-8976
url https://repositorio.unal.edu.co/handle/unal/66486
http://bdigital.unal.edu.co/67514/
dc.language.iso.spa.fl_str_mv spa
language spa
dc.relation.spa.fl_str_mv https://revistas.unal.edu.co/index.php/estad/article/view/65654
dc.relation.ispartof.spa.fl_str_mv Universidad Nacional de Colombia Revistas electrónicas UN Revista Colombiana de Estadística
Revista Colombiana de Estadística
dc.relation.references.spa.fl_str_mv Bolbolian Ghalibaf, Mohammad (2018) Kernel Function in Local Linear Peters-Belson Regression. Revista Colombiana de Estadística, 41 (2). pp. 235-249. ISSN 2389-8976
dc.rights.spa.fl_str_mv Derechos reservados - Universidad Nacional de Colombia
dc.rights.coar.fl_str_mv http://purl.org/coar/access_right/c_abf2
dc.rights.license.spa.fl_str_mv Atribución-NoComercial 4.0 Internacional
dc.rights.uri.spa.fl_str_mv http://creativecommons.org/licenses/by-nc/4.0/
dc.rights.accessrights.spa.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv Atribución-NoComercial 4.0 Internacional
Derechos reservados - Universidad Nacional de Colombia
http://creativecommons.org/licenses/by-nc/4.0/
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.format.mimetype.spa.fl_str_mv application/pdf
dc.publisher.spa.fl_str_mv Universidad Nacional de Colombia - Sede Bogotá - Facultad de Ciencias - Departamento de Estadística
institution Universidad Nacional de Colombia
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spelling Atribución-NoComercial 4.0 InternacionalDerechos reservados - Universidad Nacional de Colombiahttp://creativecommons.org/licenses/by-nc/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Bolbolian Ghalibaf, Mohammad0333f80f-3125-4dfd-97f4-3a00ce2758363002019-07-03T02:13:16Z2019-07-03T02:13:16Z2018-07-01ISSN: 2389-8976https://repositorio.unal.edu.co/handle/unal/66486http://bdigital.unal.edu.co/67514/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.application/pdfspaUniversidad Nacional de Colombia - Sede Bogotá - Facultad de Ciencias - Departamento de Estadísticahttps://revistas.unal.edu.co/index.php/estad/article/view/65654Universidad Nacional de Colombia Revistas electrónicas UN Revista Colombiana de EstadísticaRevista Colombiana de EstadísticaBolbolian Ghalibaf, Mohammad (2018) Kernel Function in Local Linear Peters-Belson Regression. Revista Colombiana de Estadística, 41 (2). pp. 235-249. ISSN 2389-897651 Matemáticas / Mathematics31 Colecciones de estadística general / StatisticsKernel FunctionLocal Linear Peters-Belson RegressionMajority GroupMinority GroupWelch's Approximation.Aproximación de Welchfunción kernelregresión lineal localKernel Function in Local Linear Peters-Belson RegressionArtículo de revistainfo:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501http://purl.org/coar/resource_type/c_2df8fbb1http://purl.org/coar/version/c_970fb48d4fbd8a85Texthttp://purl.org/redcol/resource_type/ARTORIGINAL65654-390959-1-PB.pdfapplication/pdf410073https://repositorio.unal.edu.co/bitstream/unal/66486/1/65654-390959-1-PB.pdfb5ca8ca3b18de586ec17d30b61ede9cfMD51THUMBNAIL65654-390959-1-PB.pdf.jpg65654-390959-1-PB.pdf.jpgGenerated Thumbnailimage/jpeg6240https://repositorio.unal.edu.co/bitstream/unal/66486/2/65654-390959-1-PB.pdf.jpg9295e84b27a740941c131a998954bea1MD52unal/66486oai:repositorio.unal.edu.co:unal/664862023-05-25 23:02:54.57Repositorio Institucional Universidad Nacional de Colombiarepositorio_nal@unal.edu.co