Dissertations / Theses on the topic 'Transformations de Box-Cox'

Random effect models have become a mainstream statistical technique over the last decades; and the same can be said for response transformation models such as the Box-Cox transformation. The latter ensures that the assumptions of normality and of homoscedasticity of the response distribution are fulfilled, which are essential conditions for the use of a linear model or a linear mixed model. However, methodology for response transformation and simultaneous inclusion of random effects has been developed and implemented only scarcely, and is so far restricted to Gaussian random effects. The first aim of this thesis is to develop such methodology, thereby not requiring parametric assumptions on the distribution of the random effects. This is achieved by extending the “Nonparametric Maximum Likelihood” towards a “Nonparametric Profile Maximum Likelihood” (NPPML) technique. The implemented techniques allow to deal with overdispersion as well as two-level data scenarios in general linear models. The second part of this thesis considers the transformation of mixed-effects logistic models, with the aim of improving model fit. In binary data, link functions other than the logit can be used to connect predictors with the response. The Box-Cox transformation is used in mixed–effects binary regression models as an alternative link function for linearization purposes. The NPPML approach is used similarly as before, with some adjustments. The proposed approach is implemented in the R package boxcoxmix. Simulation studies and applications on real data are carried out to study the performance of this approach.

This Thesis deals with the using of transformations in model of regression analysis. The first part of the Thesis summarizes the theoretical findings of the regression models, assumption of these models and the possibility of using different types of transformations in the event non-compliance of regression models. The practical part of this Thesis deals with regression analysis of real dataset on school readiness of children from the district of Kolín in 2013 and using transformations in the selected regression model.

Conselho Nacional de Desenvolvimento Científico e Tecnológico<br>The path analysis allows evaluation of the direct and indirect effects of the explicative variables on variable of interest, through the breakdown of the correlation coefficients. In order to make the results obtained through the path analysis reliable, some assumptions must be met. Thus, the objectives of this study were to verify the normality and the multicollinearity interference in the corn path analysis and compare alternative methods for estimating the path coefficients. Data from 44 trials of corn cultivars was used, carried out in the state of Rio Grande do Sul, between the crop years 2002/03 and 2004/05. In each cultivar, of each trial, were measured (number of days until the male flowering, plant height, ear insertion height, relative position of the ear, number of plants, number of ears and prolificacy) and the main variable (grain yield). For each trial, descriptive statistics were calculated and univariate and multivariate normality diagnoses were conducted using the Shapiro-Wilk test and the Shapiro-Wilk multivariate generalized by Royston test, respectively. Thereupon, in the trials data that did not present a normal distribution, a transformation of the data by the Box-Cox family of transformations was carried out. The correlation coefficients between the seven explicative variables (correlation matrix X'X) and the correlation coefficients of each explicative variable with the grain yield (correlation matrix X'Y) were calculated for the original and transformed data. Then, the multicollinearity was diagnosed in the correlation matrix X'X, using four methods: variance inflation factor, tolerance, the condition number and the matrix determinant. Finally, the path analysis was performed, using the normal equations system X X �� = X Y, in three forms: traditional path analysis, path analysis under multicollinearity and traditional path analysis, with elimination of variables. The data transformation, to obtain multivariate normality, contributes to the degree of multicollinearity decrease and in the stabilization of the direct effects in path analysis with high degree of multicollinearity. The high degrees of multicollinearity adverse effects in the estimation of the direct effects in path analysis are larger than the multivariate non-normality. The traditional path analysis, with elimination of variables, is more appropriate than the path analysis under multicollinearity.<br>A análise de trilha permite avaliar os efeitos diretos e indiretos de variáveis explicativas sobre a variável de interesse, por meio do desdobramento dos coeficientes de correlação. Para que os resultados gerados pela análise de trilha apresentem confiabilidade adequada, alguns pressupostos devem ser atendidos. Assim, os objetivos deste trabalho foram: verificar a interferência da não-normalidade multivariada e da multicolinearidade em análise de trilha na cultura de milho e, comparar métodos alternativos de estimação dos coeficientes de trilha. Foram utilizados dados de 44 ensaios de competição de cultivares de milho, conduzidos no estado do Rio Grande do Sul, entre os anos agrícolas de 2002/03 e 2004/05. Em cada cultivar, de cada ensaio, foram mensuradas sete variáveis explicativas (número de dias até o florescimento masculino, estatura de plantas, altura de inserção da espiga, posição relativa da espiga, número de plantas, número de espigas e prolificidade) e a variável principal (produtividade de grãos). Para cada ensaio, foram calculadas estatísticas descritivas e realizado o diagnóstico de normalidade uni e multivariada, por meio dos testes de Shapiro-Wilk e de Shapiro-Wilk multivariado generalizado por Royston, respectivamente. A seguir, nos dados dos ensaios que não apresentaram distribuição normal, foi realizada a transformação dos dados com a utilização da família de transformações Box-Cox. Para os dados originais e os dados transformados, foram calculados os coeficientes de correlação entre as sete variáveis explicativas (matriz de correlação X X) e os coeficientes de correlação de cada variável explicativa com a produtividade de grãos (matriz de correlação X Y). A seguir, foi realizado o diagnóstico de multicolinearidade na matriz de correlação X X, por meio de quatro métodos: fator de inflação de variância, tolerância, número de condição e determinante da matriz. Por fim, foi realizada a análise de trilha, com a utilização do sistema de equações normais X X �� = X Y, por três formas: análise de trilha tradicional, análise de trilha sob multicolinearidade e análise de trilha tradicional, com eliminação de variáveis. A transformação de dados, a fim de obter a normalidade multivariada, contribui para a redução do grau de multicolinearidade e na estabilização das estimativas dos efeitos diretos em análise de trilha com alto grau de multicolinearidade. Os efeitos adversos do alto grau de multicolinearidade na estimativa dos efeitos diretos de análises de trilha são maiores que a não-normalidade multivariada. A análise de trilha tradicional, com eliminação de variáveis, é mais adequada que a análise de trilha sob multicolinearidade.

Orientador: Luzia Aparecida Trinca<br>Resumo: Nas mais diversas áreas do conhecimento se procura aumentar a eficiência dos delineamentos experimentais, principalmente, para minimizar os custos das pesquisas. O uso dos delineamentos ótimos, com seus diferentes critérios de otimização, é fundamental para se obter resultados que maximizam a informação em estudos experimentais. A maioria dos métodos pressupõe homogeneidade de variâncias, a qual nem sempre é veri cada no conjunto de dados. O objetivo deste trabalho é desenvolver uma metodologia para construção de delineamentos ótimos exatos e cientes em situações de variância não homogênea. Assume-se que linearidade e homoscedasticidade são obtidas via o uso de transformações da família Box-Cox e, além de critérios de otimização puros, critérios compostos que combinam duas propriedades são propostos. Resultados para vários exemplos sob os modelos de primeira e segunda ordem são obtidos e discutidos.<br>Abstract: In several areas of knowledge we seek to increase the efficiency of experimental designs, mainly in order to minimize the costs of reaserch. The use of optimal design with different optimization criteria is fundamental to obtain results that maximize the information in experimental studies. Most of the methods assume homogeneity of variances, which is not always verified in the data set. The goal of this work is to develop a methodology to construct exact optimal or efficient designs in situations of nonhomogeneous variance. It is assumed that application of a transformation from the Box-Cox family accomplish both linearity and homocedasticity. Pure design criterion as well as compound criteria using two desired properties are used. Results for several examples assuming first and second order models are presented and discussed.<br>Doutor

This paper explores the fit of a stochastic volatility model, in which the Box-Cox transformation of the squared volatility follows an autoregressive Gaussian distribution, to the continuously compounded daily returns of the Australian stock index. Estimation was difficult, and over-fitting likely, because more variables are present than data. We developed a revised model that held a couple of these variables fixed and then, further, a model which reduced the number of variables significantly by grouping trading days. A Metropolis-Hastings algorithm was used to simulate the joint density and derive estimated volatilities. Though autocorrelations were higher with a smaller Box-Cox transformation parameter, the fit of the distribution was much better.

Le dynamisme du secteur aérien canadien amène Transports Canada à réviser régulièrement ses techniques de modélisation du trafic de passagers afin d’améliorer la performance prédictive de ses modèles. Ce travail explore différentes versions d’un modèle PODM (Passanger Origin-Destination Model) que Transports Canada utilise pour prévoir le trafic de passagers entre une origine et une destination à l’intérieur du Canada avec des données de panel (i.e. longitudinales et transversales). Deux formes paramétriques (log-linéaire et Box-Cox) sont estimées dans leurs versions empilées, avec des effets fixes/aléatoires et avec des coefficients individuels variables (fixes/aléatoires). Nous proposons également des estimations non paramétriques à noyaux pour explorer les non-linéarités qui caractérisent la relation entre le nombre de passagers par couple origine-destination et le prix du billet, le PIB des zones d’origine et de destination, la durée en voiture du trajet et la fréquence des vols. L’hypothèse d’empilement des données et les formes fonctionnelles postulées se révèlent statistiquement inadéquates. La prise en compte de l’hétérogénéité des trajets et des effets temporels par l’inclusion d’effets fixes/aléatoires dans les modèles paramétriques est également rejetée par nos tests. Les modèles à coefficients variables individuels et les estimations non paramétriques se révèlent les méthodes les plus pertinentes pour capturer l’hétérogénéité entre trajets, les chocs temporels ou les non-linéarités présentes dans les relations d’intérêt. Mots clés : Box-Cox, transport aérien, trafic de passagers, origine-destination, Transports Canada, non paramétrique, panels.

The focus of this thesis is an investigation of ways to detect weak dependence between two random variables X and Y. Our approach is to design tests for correlation rather than testing for dependence directly, since X and Y are not independent if they are not uncorrelated. We examined the magnified Pearson correlation after the Box-Cox transformation to determine whether X and Y are dependent. The results indicated that our approach not only has the potential to detect and evaluate the weak dependence cases that have previously been intractable, but also is conceptually simple and easy to implement.

The diploma thesis is focused on process stability and capability assessment. It describes certain types of control charts, basic capability indices as well as Box-Cox transformation. The practical part of the study is concerned with applying control charts on generated data and consequently on real data. By this, it focuses on comparing various methods of estimating sample standard deviation and on the impact of non-compliance with the assumption of normal distribution of process variable on process stability and capability assessment.

Made available in DSpace on 2015-03-26T13:32:19Z (GMT). No. of bitstreams: 1 texto completo.pdf: 508483 bytes, checksum: ed19e15dac174ba29cb7068c7f83a289 (MD5) Previous issue date: 2013-04-26<br>The objective of this work was to verify the efficiency of Box-Cox and Blom scores transformations in correcting the phenotypic heterogeneity of variance adjusted weights of cattle Tabapuã the Brazilian Northeast to the factors producing regions, ages and sex. We used data Tabapuã the Brazilian Northeast, collected from 1970, from the control of weight development Brazilian Association of Zebu Breeders (ABCZ) with information concerning the weights adjusted to 205, 365 and 550 days of age. The Box-Cox and Blom scores transformations were used in an attempt to correct the heterogeneity of variances for the factors of production regions, ages and sex. Bartlett's test was applied before and after the transformation of the data to see if there was a reduction of heterogeneity of phenotypic variances. The Blom scores transformation was effective in reducing the coefficients of skewness and kurtosis and was more appropriate than the Box-Cox transformation to correct the phenotypic heterogeneity of variance between production regions, ages and sex, since produced significantly more favorable results.<br>O objetivo deste trabalho foi verificar a eficiência das transformações de Box- Cox e escores de Blom na correção da heterogeneidade de variâncias fenotípicas dos pesos ajustados de bovinos da raça Tabapuã do Nordeste brasileiro para os fatores regiões de produção, idades e sexos. Foram utilizados dados da raça Tabapuã do Nordeste brasileiro, coletados a partir de 1970, provenientes do controle de desenvolvimento ponderal da Associação Brasileira de Criadores de Zebuíno (ABCZ) com informações relativas a pesos ajustados para 205, 365 e 550 dias de idade. As transformações em escores de Blom e Box-Cox foram utilizadas na tentativa de corrigir a heterogeneidade de variâncias para os fatores regiões de produção, idades e sexos. O teste de Bartlett foi aplicado antes e após a transformação dos dados para verificar se houve redução da heterogeneidade de variâncias fenotípicas. A transformação em escores de Blom foi efetiva na redução dos coeficientes de assimetria e curtose e mostrou-se mais adequada do que a transformação de Box-Cox para correção da heterogeneidade de variâncias fenotípicas entre regiões de produção, idades e sexos, uma vez que apresentou um maior número de resultados favoráveis.

Turkey has very different geomorphologic, hydrologic and climatic conditions, so the runoff coefficient should be different from one basin to another. But only one constant value, which is 0.37, is being used for all the basins in Turkey. In this thesis, monthly, seasonal and annual runoff coefficients of 48 sub-basins in western and southern part of Anatolia are determined by using synchronous and average rainfall, runoff data of 26 year record period. Their temporal and spatial distributions are investigated. The relationship between the basin parameters and the runoff coefficient are also examined. Some of the basins have unrealistic large runoff coefficients, therefore excluded from the analyses. The basin boundaries and parameters are determined by using Geograhic Information System (GIS), and areal average precipitations are found by a program written in visual basic language that uses ArcObjects. The Box-Cox transformed data are used in regression analysis. There are a number of dams in the region, which affect the natural flow. Such streams are found and their sub-basins are not used in the analyses. The results revealed that there is not a strong the relationship between the basin parameters and annual and seasonal runoff coefficients for the whole region, but there are significant relations between them for some basins.

Nesta tese são desenvolvidos três estudos sobre o risco associado aos acidentes de trânsito, com o objetivo de avaliar como a população o percebe, e o valor que estaria disposta a pagar para reduzi-lo. As análises foram feitas com duas diferentes metodologias econométricas e dois diferentes conjuntos de dados da população de Porto Alegre. O primeiro estudo procurou avaliar que fatores de risco contribuem para aumentar a gravidade dos acidentes de trânsito, utilizando dados de acidentes de trânsito ocorridos na cidade de Porto Alegre no período 2000-2008, através de modelos logit ordenados generalizados. Os resultados indicam que a maioria das vítimas feridas em acidentes de trânsito são condutores jovens, do sexo masculino e que estavam em motocicletas ou cujo acidente foi um choque contra obstáculos. Contudo, as vítimas fatais têm maior probabilidade de morte são os pedestres, com mais de 60 anos de idade. Os acidentes com maior gravidade ocorrem em maior proporção a noite ou finais de semana, em locais mais afastados do centro da cidade, o que sugere comportamento associado à alta velocidade e uso de substâncias psicoativas como álcool. Para os demais estudos utilizaram-se dados de um survey feito com a população de Porto Alegre em 2009. O segundo estudo avalia como as características sócio-demográficas, a experiência no trânsito e a informação recebida, afetam a percepção do risco e o comportamento no trânsito. Os resultados indicam que os indivíduos que tem risco maior de morte no trânsito subestimam seu próprio risco e vice-versa; e que os mais jovens têm maior percepção deste risco, assim como os que tiveram experiência de acidente de trânsito ou passam mais tempo expostos a ele. O risco do consumo de bebidas alcoólicas associado ao trânsito, no entanto é percebido maior pelos idosos, mulheres, não bebedores ou quem não tem comportamento de risco, assim como pelos que têm mais informação do risco. Da mesma maneira, o comportamento de risco no trânsito associado ao consumo de álcool está negativamente relacionado a percepção deste risco e a idade. O terceiro estudo estimou a disposição a pagar ( ) dos entrevistados pela redução no seu próprio risco de sofrer lesões em um acidente de trânsito e o valor de uma vida estatística ( ), utilizando modelos lineares e não-lineares ajustados através de uma transformação Box-Cox. Os resultados indicam que a esta relacionada de forma decrescente com a idade e com a não utilização de dispositivos de segurança, mas aumenta com a renda, o tempo de exposição ao trânsito, a experiência com acidentes, para as mulheres e para os que têm dependentes. O valor médio eliciado da para reduzir a zero o risco das lesões mais graves, que resultam em morte, implicou em de cerca de R$ 13,4 milhões (US$7,3 milhões) - valor menor, porém comparável ao encontrado para países desenvolvidos e em estudo para o Brasil.<br>This thesis develops three studies on the risk associated with traffic accidents, in order to assess how people perceive it and the value they would be willing to pay to reduce it. The analysis was made with two different econometric methods and two different sets of data from Porto Alegre's population. The first study to assess at risk factors that contribute to increased severity of accidents, using data obtained from traffic accidents in the city of Porto Alegre between the years 2000 and 2008, and applying the generalized ordered logit. The results indicate that most of the victims injured in accidents are young drivers, males, motorcyclists and whose crash was a “collision with obstacles”. However, fatal victims have a different profile: they are pedestrians, over 60 years old. The most serious accidents occur in greater proportions at nights or weekends, at locations further away from the city center, which suggests behavior associated with high speed driving and the use of psychoactive substances, such as alcohol. The other two studies used data from a survey done with the population of Porto Alegre in 2009. The second study evaluates how socio-demographic characteristics, traffic experience and the information received about the risks of driving under the influence of alcohol, affect risk perception and behavior in the traffic. The results indicate that individuals who have greater risk of dying in traffic, underestimate their own risk and vice versa; and that young people as well as those who have been in an accident or those who spend a lot of time in traffic, have a greater perception of their risk. On the other hand, the risk of alcohol consumption associated with traffic, is perceived better by older people, women, non-drinkers, people without risky behavior, and those who are more aware of the risks of driving under the influence of alcohol. Similarly, risky behavior in traffic, related to alcohol consumption, is inversely proportional to perception of risk and to age. The third study estimated the respondents' willingness to pay ( ) for the reduction in their risk of suffering injuries in a traffic accident, as well as the value of a statistical life ( ), using linear and nonlinear models adjusted by the Box-Cox transformation. The results indicate that the decreases with age and with not using safety devices, but increases with income, exposure to traffic, and the accidents experience, for women and for those who have dependents. The average value elicited by to reduce to zero the risk of severe injuries that result in death, implied a of about R$13.4 million (US$ 7.3 million) - lower, but still a comparable value to that found in developed countries, and studied in Brazil.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1990.<br>Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves 77-80).

Thesis (Ph. D.)--University of Wisconsin--Madison, 1994.<br>Typescript. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves 80-83).

碩士<br>國立成功大學<br>統計學系碩博士班<br>93<br>The main use of Box-Cox transformation is to transformation data to be approximately normal distributed. While one or a few cases can greatly influence the estimation of transformation coefficient lambda. To detect influential cases, several methods have been suggested. So far, diagnostics for the transformation coefficient lambda is mainly on univariate data and regression problem.With current computing capability, we can replace complicated derivation by fast computing program,which allow us to extend the methodology to multiivariate cases. Among these, graphic presentation provides detailed and further insight through visual examination. All the computing and graphics are carried out by freeware R.

碩士<br>輔仁大學<br>應用統計學研究所<br>98<br>Discriminant analysis has been widely used in a variety of areas, such as medicine, finance and quality control, etc. Based on Fisher’s linear discriminant analysis(FLDA), this study is restricted in discussion of the discriminant analysis while the number of population is two. To improve the FLDA, this study proposes to use the Box-Cox transformation to transform the data and constructs “a family of discriminant functions” and “a family of discriminant rules”. When all the values of power transformation are equal to 1, the proposed approach becomes the FLDA.Under this concept, we propose two new methods, “the method of maximum objective function” a nd “the method of minimum APER” to find optimal values of power transformation. Simulation results show that when the data are non-symmetrically distributed, the two new methods have better performance than FLDA.

碩士<br>立德管理學院<br>應用資訊研究所<br>92<br>The Artificial Neural Network (ANN) has developed for many years. The type of model and its architecture is gradually substantial. It has a widespread application, like as pattern recognition, cluster analysis, forecasting, etc. The ANN applied to forecasting has been approved by many specialists and scholars from many fields of science. Among the supervised networks, the Back Propagation Network (BPN) model is the most popular and it is the basis for model improvement in this study. The characteristic of the BPN model is powerful on operation ability and easy to use. To improve the accuracy of the BPN model, the Multilayer Functional-Link Network (MFLN) model is developed to strengthen the BPN model. Nevertheless, it is hard to explain the physical meaning with neurons of the logarithmic and exponential transformation. Two scholars, Box and Cox, develop the nonlinear Box-Cox transformation (BCT) that is more flexible. The BCT-MFLN model, the improvement of MFLN model, is proposed to combine the learning ability of MFLN and the suitable transformation parameter. The case studies show that the BCT-MFLN model is better. Furthermore, considering the concise need of the complexity of the neural network and the learning epoch, the BCT is directly introduced into the BPN model, it is so-called the BCT-BPN model. It not only reduces the whole complexity of the MFLN model but also achieves an objective of model parsimony and learning-number reduction. To compare and analysis the BPN, MFLN, BCT-MFLN and BCT-BPN models, several evaluation indices are selected for the study. The Overall Performance Intensity (OPI) is proposed to sum up all indices and it is subjective to evaluate the different models. From lots of case studies, the models with BCT (BCT-MFLN、BCT-BPN) can improve the learning rate and accelerate the convergence. By means of the OPI analysis, it could be more subjective to assure the accuracy of models with Box-Cox Transformation.

碩士<br>國立中央大學<br>統計研究所<br>95<br>In order to quickly extract information on the life of a product, accelerated life-tests are usually employed. In this thesis, we discuss a k-stage step-stress accelerated life-test with M stress variables when the underlying data are progressively Type-I group censored. The life-testing model assumed is an exponential distribution with a link function that relates the failure rate and the stress variables in a linear way under the Box-Cox transformation, and a cumulative exposure model for modelling the effect of stress changes. The classical maximum likelihood method as well as a fully Bayesian method based on the Markov chain Monte Carlo (MCMC) technique are developed for inference on all the parameters of this model. Numerical examples are presented to illustrate all the methods of inference developed here, and a comparison of the ML and Bayesian methods is also carried out.

Le but de ce mémoire de maîtrise est de décrire les propriétés de la loi double Pareto-lognormale, de montrer comment on peut introduire des variables explicatives dans le modèle et de présenter son large potentiel d'applications dans le domaine de la science actuarielle et de la finance. Tout d'abord, nous donnons la définition de la loi double Pareto-lognormale et présentons certaines de ses propriétés basées sur les travaux de Reed et Jorgensen (2004). Les paramètres peuvent être estimés en utilisant la méthode des moments ou le maximum de vraisemblance. Ensuite, nous ajoutons une variable explicative à notre modèle. La procédure d'estimation des paramètres de ce mo-\\dèle est également discutée. Troisièmement, des applications numériques de notre modèle sont illustrées et quelques tests statistiques utiles sont effectués.<br>The purpose of this Master's thesis is to describe the double Pareto-lognormal distribution, show how the model can be extended by introducing explanatory variables in the model and present its large potential of applications in actuarial science and finance. First, we give the definition of the double Pareto-lognormal distribution and present some of its properties based on the work of Reed and Jorgensen (2004). The parameters could be estimated by using the method of moments or maximum likelihood. Next, we add an explanatory variable to our model. The procedure of estimation for this model is also discussed. Finally, some numerical applications of our model are illustrated and some useful statistical tests are conducted.