Teste Bootstrap de normalidade univariada baseado na entropia
Autor(a) principal: | |
---|---|
Data de Publicação: | 2018 |
Tipo de documento: | Dissertação |
Idioma: | por |
Título da fonte: | Repositório Institucional da UFLA |
Texto Completo: | http://repositorio.ufla.br/jspui/handle/1/29501 |
Resumo: | The behaviour of many phenomena, in many areas of the knowledge, is described by the normal distribution of probability. When a random sample of population is taken, in the univariate case, it is common to assume that the data or residues of certain model are normally distributed. This assumption of normality must be verified through application of a statistical test. The entropy can be understood as a measure of the amount of randomness of an information system, and used to measure the uncertainty of a random variable. It is also being used for testing normality. This study is aimed to propose univariate normality tests based on entropy. These tests are computationally intensive procedures based on parametric bootstrap technique. In addition, the power of the Shapiro-Wilk normality test (TW ) was compared with the proposed univariate normality tests (T KB, T KRB 1 , T KRB 2 , T KRB C ). Computational intensive alternatives based on parametric bootstrap allowed to circumvent the limitations of sample sizes n of the existing entropy-based tests, which allow a maximum of n = 100 and also to overcome the problem of non-invariance of one of the options. The proposed tests showed adequate control of the type I error rates, if they were accurate, with sizes equal to the level of nominal significance a . Regarding performance under alternative hypotheses, at least one of the T KB, T KRB 1 , T KRB 2 , T KRB C , tests demonstrated its supremacy. Thus, we can recommend them, since they generally exceeded the concurrent best-performance test, chosen to be the reference test, the Shapiro-Wilk (TW ) test, although, still prevailing the idea of non-existence of a uniformly more powerful test for all the alternative hypotheses studied. Proposals may be used on samples over 5;000, which is one of its main virtues in relation to the test used as a reference. |
id |
UFLA_2d8fee814d06db18f3917fbf095d7917 |
---|---|
oai_identifier_str |
oai:localhost:1/29501 |
network_acronym_str |
UFLA |
network_name_str |
Repositório Institucional da UFLA |
repository_id_str |
|
spelling |
Teste Bootstrap de normalidade univariada baseado na entropiaBootstrap paramétricoEntropiaTeste de Shapiro-WilkParametric bootstrapEntropyShapiro-Wilk testEstatísticaThe behaviour of many phenomena, in many areas of the knowledge, is described by the normal distribution of probability. When a random sample of population is taken, in the univariate case, it is common to assume that the data or residues of certain model are normally distributed. This assumption of normality must be verified through application of a statistical test. The entropy can be understood as a measure of the amount of randomness of an information system, and used to measure the uncertainty of a random variable. It is also being used for testing normality. This study is aimed to propose univariate normality tests based on entropy. These tests are computationally intensive procedures based on parametric bootstrap technique. In addition, the power of the Shapiro-Wilk normality test (TW ) was compared with the proposed univariate normality tests (T KB, T KRB 1 , T KRB 2 , T KRB C ). Computational intensive alternatives based on parametric bootstrap allowed to circumvent the limitations of sample sizes n of the existing entropy-based tests, which allow a maximum of n = 100 and also to overcome the problem of non-invariance of one of the options. The proposed tests showed adequate control of the type I error rates, if they were accurate, with sizes equal to the level of nominal significance a . Regarding performance under alternative hypotheses, at least one of the T KB, T KRB 1 , T KRB 2 , T KRB C , tests demonstrated its supremacy. Thus, we can recommend them, since they generally exceeded the concurrent best-performance test, chosen to be the reference test, the Shapiro-Wilk (TW ) test, although, still prevailing the idea of non-existence of a uniformly more powerful test for all the alternative hypotheses studied. Proposals may be used on samples over 5;000, which is one of its main virtues in relation to the test used as a reference.O comportamento de muitos fenômenos, em muitas áreas do saber, é descrito pela distribuição normal de probabilidade. Ao se retirar uma amostra aleatória de uma população, no caso univariado, é comum pressupor que os dados ou resíduos de algum modelo sejam normalmente distribuídos. Essa pressuposição de normalidade deve ser verificada por meio da aplicação de testes estatísticos. A entropia pode ser entendida como uma medida da quantidade de aleatoriedade de um sistema de informação, sendo usada para medir a incerteza de uma variável aleatória. Ela tem sido também utilizada para testar a normalidade. Este trabalho teve como objetivo propor testes de normalidade univariada baseados na entropia. Estes testes são essencialmente procedimentos computacionalmente intensivos baseados na técnica bootstrap paramétrico. Além disso, comparou-se o poder do teste de normalidade Shapiro-Wilk (TW ) com os testes de normalidade univariada propostos (T KB, T KRB 1 , T KRB 2 , T KRB C ). As alternativas computacionalmente intensivas, baseada em bootstrap paramétrico permitiram contornar as limitações de tamanhos amostrais n dos testes baseados em entropia existentes, que permitem no máximo n = 100 e também contornar o problema da não invariância de uma das opções. Os testes propostos apresentaram controle adequado das taxas de erro tipo I, se mostrando exatos, com tamanhos iguais ao nível de significância nominal a . Em relação ao desempenho sob as hipóteses alternativas, ao menos um dos testes T KB, T KRB 1 , T KRB 2 e T KRB C , esteve quase sempre como o mais poderoso. Assim, pode-se recomendá-los, pois estes superaram, de maneira geral, o teste sendo concorrente de melhor desempenho, escolhido para ser o teste de referência, o teste de Shapiro-Wilk (TW ) mas, prevalecendo a ideia ainda da não existência de um teste uniformemente mais poderoso para todas as hipóteses alternativas estudadas. As propostas podem ser usadas em amostras superiores a 5:000, que é uma das suas principais virtudes em relação ao teste usado como referência.Universidade Federal de LavrasPrograma de Pós-Graduação em Estatística e Experimentação AgropecuáriaUFLAbrasilDepartamento de Ciências ExatasFerreira, Daniel FurtadoOliveira, Deive Ciro deGuimarães, Paulo Henriques SalesPascoal, Neto2018-06-25T11:52:11Z2018-06-25T11:52:11Z2018-06-222018-06-15info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesisapplication/pdfPASCOAL, N. Teste Bootstrap de normalidade univariada baseado na entropia. 2018. 70 p. Dissertação (Mestrado em Estatística e Experimentação Agropecuária)-Universidade Federal de Lavras, Lavras, 2018.http://repositorio.ufla.br/jspui/handle/1/29501porinfo:eu-repo/semantics/openAccessreponame:Repositório Institucional da UFLAinstname:Universidade Federal de Lavras (UFLA)instacron:UFLA2019-06-24T16:09:20Zoai:localhost:1/29501Repositório InstitucionalPUBhttp://repositorio.ufla.br/oai/requestnivaldo@ufla.br || repositorio.biblioteca@ufla.bropendoar:2019-06-24T16:09:20Repositório Institucional da UFLA - Universidade Federal de Lavras (UFLA)false |
dc.title.none.fl_str_mv |
Teste Bootstrap de normalidade univariada baseado na entropia |
title |
Teste Bootstrap de normalidade univariada baseado na entropia |
spellingShingle |
Teste Bootstrap de normalidade univariada baseado na entropia Pascoal, Neto Bootstrap paramétrico Entropia Teste de Shapiro-Wilk Parametric bootstrap Entropy Shapiro-Wilk test Estatística |
title_short |
Teste Bootstrap de normalidade univariada baseado na entropia |
title_full |
Teste Bootstrap de normalidade univariada baseado na entropia |
title_fullStr |
Teste Bootstrap de normalidade univariada baseado na entropia |
title_full_unstemmed |
Teste Bootstrap de normalidade univariada baseado na entropia |
title_sort |
Teste Bootstrap de normalidade univariada baseado na entropia |
author |
Pascoal, Neto |
author_facet |
Pascoal, Neto |
author_role |
author |
dc.contributor.none.fl_str_mv |
Ferreira, Daniel Furtado Oliveira, Deive Ciro de Guimarães, Paulo Henriques Sales |
dc.contributor.author.fl_str_mv |
Pascoal, Neto |
dc.subject.por.fl_str_mv |
Bootstrap paramétrico Entropia Teste de Shapiro-Wilk Parametric bootstrap Entropy Shapiro-Wilk test Estatística |
topic |
Bootstrap paramétrico Entropia Teste de Shapiro-Wilk Parametric bootstrap Entropy Shapiro-Wilk test Estatística |
description |
The behaviour of many phenomena, in many areas of the knowledge, is described by the normal distribution of probability. When a random sample of population is taken, in the univariate case, it is common to assume that the data or residues of certain model are normally distributed. This assumption of normality must be verified through application of a statistical test. The entropy can be understood as a measure of the amount of randomness of an information system, and used to measure the uncertainty of a random variable. It is also being used for testing normality. This study is aimed to propose univariate normality tests based on entropy. These tests are computationally intensive procedures based on parametric bootstrap technique. In addition, the power of the Shapiro-Wilk normality test (TW ) was compared with the proposed univariate normality tests (T KB, T KRB 1 , T KRB 2 , T KRB C ). Computational intensive alternatives based on parametric bootstrap allowed to circumvent the limitations of sample sizes n of the existing entropy-based tests, which allow a maximum of n = 100 and also to overcome the problem of non-invariance of one of the options. The proposed tests showed adequate control of the type I error rates, if they were accurate, with sizes equal to the level of nominal significance a . Regarding performance under alternative hypotheses, at least one of the T KB, T KRB 1 , T KRB 2 , T KRB C , tests demonstrated its supremacy. Thus, we can recommend them, since they generally exceeded the concurrent best-performance test, chosen to be the reference test, the Shapiro-Wilk (TW ) test, although, still prevailing the idea of non-existence of a uniformly more powerful test for all the alternative hypotheses studied. Proposals may be used on samples over 5;000, which is one of its main virtues in relation to the test used as a reference. |
publishDate |
2018 |
dc.date.none.fl_str_mv |
2018-06-25T11:52:11Z 2018-06-25T11:52:11Z 2018-06-22 2018-06-15 |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/masterThesis |
format |
masterThesis |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
PASCOAL, N. Teste Bootstrap de normalidade univariada baseado na entropia. 2018. 70 p. Dissertação (Mestrado em Estatística e Experimentação Agropecuária)-Universidade Federal de Lavras, Lavras, 2018. http://repositorio.ufla.br/jspui/handle/1/29501 |
identifier_str_mv |
PASCOAL, N. Teste Bootstrap de normalidade univariada baseado na entropia. 2018. 70 p. Dissertação (Mestrado em Estatística e Experimentação Agropecuária)-Universidade Federal de Lavras, Lavras, 2018. |
url |
http://repositorio.ufla.br/jspui/handle/1/29501 |
dc.language.iso.fl_str_mv |
por |
language |
por |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
application/pdf |
dc.publisher.none.fl_str_mv |
Universidade Federal de Lavras Programa de Pós-Graduação em Estatística e Experimentação Agropecuária UFLA brasil Departamento de Ciências Exatas |
publisher.none.fl_str_mv |
Universidade Federal de Lavras Programa de Pós-Graduação em Estatística e Experimentação Agropecuária UFLA brasil Departamento de Ciências Exatas |
dc.source.none.fl_str_mv |
reponame:Repositório Institucional da UFLA instname:Universidade Federal de Lavras (UFLA) instacron:UFLA |
instname_str |
Universidade Federal de Lavras (UFLA) |
instacron_str |
UFLA |
institution |
UFLA |
reponame_str |
Repositório Institucional da UFLA |
collection |
Repositório Institucional da UFLA |
repository.name.fl_str_mv |
Repositório Institucional da UFLA - Universidade Federal de Lavras (UFLA) |
repository.mail.fl_str_mv |
nivaldo@ufla.br || repositorio.biblioteca@ufla.br |
_version_ |
1815439085105315840 |