A Study of Seven Asymmetric Kernels for the Estimation of Cumulative Distribution Functions
In this paper, we complement a study recently conducted in a paper of H.A. Mombeni, B. Masouri and M.R. Akhoond by introducing five new asymmetric kernel c.d.f. estimators on the half-line <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"&...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-10-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/9/20/2605 |
| _version_ | 1797513972407074816 |
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| author | Pierre Lafaye de Micheaux Frédéric Ouimet |
| author_facet | Pierre Lafaye de Micheaux Frédéric Ouimet |
| author_sort | Pierre Lafaye de Micheaux |
| collection | DOAJ |
| description | In this paper, we complement a study recently conducted in a paper of H.A. Mombeni, B. Masouri and M.R. Akhoond by introducing five new asymmetric kernel c.d.f. estimators on the half-line <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo stretchy="false">[</mo><mn>0</mn><mo>,</mo><mo>∞</mo><mo>)</mo></mrow></semantics></math></inline-formula>, namely the Gamma, inverse Gamma, LogNormal, inverse Gaussian and reciprocal inverse Gaussian kernel c.d.f. estimators. For these five new estimators, we prove the asymptotic normality and we find asymptotic expressions for the following quantities: bias, variance, mean squared error and mean integrated squared error. A numerical study then compares the performance of the five new c.d.f. estimators against traditional methods and the Birnbaum–Saunders and Weibull kernel c.d.f. estimators from Mombeni, Masouri and Akhoond. By using the same experimental design, we show that the LogNormal and Birnbaum–Saunders kernel c.d.f. estimators perform the best overall, while the other asymmetric kernel estimators are sometimes better but always at least competitive against the boundary kernel method from C. Tenreiro. |
| first_indexed | 2024-03-10T06:25:04Z |
| format | Article |
| id | doaj.art-8babcab340c6486984fa10077f9b5bf5 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T06:25:04Z |
| publishDate | 2021-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-8babcab340c6486984fa10077f9b5bf52023-11-22T19:02:32ZengMDPI AGMathematics2227-73902021-10-01920260510.3390/math9202605A Study of Seven Asymmetric Kernels for the Estimation of Cumulative Distribution FunctionsPierre Lafaye de Micheaux0Frédéric Ouimet1School of Mathematics and Statistics, UNSW Sydney, Sydney, NSW 2052, AustraliaDepartment of Mathematics and Statistics, McGill University, Montreal, QC H3A 0B9, CanadaIn this paper, we complement a study recently conducted in a paper of H.A. Mombeni, B. Masouri and M.R. Akhoond by introducing five new asymmetric kernel c.d.f. estimators on the half-line <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo stretchy="false">[</mo><mn>0</mn><mo>,</mo><mo>∞</mo><mo>)</mo></mrow></semantics></math></inline-formula>, namely the Gamma, inverse Gamma, LogNormal, inverse Gaussian and reciprocal inverse Gaussian kernel c.d.f. estimators. For these five new estimators, we prove the asymptotic normality and we find asymptotic expressions for the following quantities: bias, variance, mean squared error and mean integrated squared error. A numerical study then compares the performance of the five new c.d.f. estimators against traditional methods and the Birnbaum–Saunders and Weibull kernel c.d.f. estimators from Mombeni, Masouri and Akhoond. By using the same experimental design, we show that the LogNormal and Birnbaum–Saunders kernel c.d.f. estimators perform the best overall, while the other asymmetric kernel estimators are sometimes better but always at least competitive against the boundary kernel method from C. Tenreiro.https://www.mdpi.com/2227-7390/9/20/2605asymmetric kernelsasymptotic statisticsnonparametric statisticsGamma kernelinverse Gamma kernelLogNormal kernel |
| spellingShingle | Pierre Lafaye de Micheaux Frédéric Ouimet A Study of Seven Asymmetric Kernels for the Estimation of Cumulative Distribution Functions Mathematics asymmetric kernels asymptotic statistics nonparametric statistics Gamma kernel inverse Gamma kernel LogNormal kernel |
| title | A Study of Seven Asymmetric Kernels for the Estimation of Cumulative Distribution Functions |
| title_full | A Study of Seven Asymmetric Kernels for the Estimation of Cumulative Distribution Functions |
| title_fullStr | A Study of Seven Asymmetric Kernels for the Estimation of Cumulative Distribution Functions |
| title_full_unstemmed | A Study of Seven Asymmetric Kernels for the Estimation of Cumulative Distribution Functions |
| title_short | A Study of Seven Asymmetric Kernels for the Estimation of Cumulative Distribution Functions |
| title_sort | study of seven asymmetric kernels for the estimation of cumulative distribution functions |
| topic | asymmetric kernels asymptotic statistics nonparametric statistics Gamma kernel inverse Gamma kernel LogNormal kernel |
| url | https://www.mdpi.com/2227-7390/9/20/2605 |
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