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Dissertations / Theses on the topic 'Skew-t'

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Published: 4 June 2021

Last updated: 6 February 2022

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1

Wang, Sheng. "Regularized skewness parameter estimation for multivariate skew normal and skew t distributions." Diss., University of Iowa, 2019. https://ir.uiowa.edu/etd/6875.

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The skewed normal (SN) distribution introduced by Azzalini has opened a new era for analyzing skewed data. The idea behind it is that it incorporates a new parameter regulating shape and skewness on the symmetric Gaussian distribution. This idea was soon extended to other symmetric distributions such as the Student's t distribution, resulting in the invention of the skew t (ST) distribution. The multivariate versions of the two distributions, i.e. the multivariate skew normal (MSN) and multivariate skew t (MST) distributions, have received considerable attention because of their ability to t s

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2

Zheng, Shimin, A. K. Gupta, and Xuefeng Liu. "A Matrix Variate Generalization of the Skew Pearson Type VII and Skew T Distribution." Digital Commons @ East Tennessee State University, 2012. https://dc.etsu.edu/etsu-works/74.

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Kantor, Benavides Alejandro. "Estudio de tres propuestas de distribución skew-t." Master's thesis, Pontificia Universidad Católica del Perú, 2015. http://tesis.pucp.edu.pe/repositorio/handle/123456789/6997.

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Este trabajo compara tres distribuciones skew-t. En particular, las propuestas por Branco y Dey (2001) y Azzalini y Capitanio (2003), Fernández y Steel (1998), y Jones y Faddy (2003). Se analiza la relación entre los parámetros y el nivel de asimetría a través de la medida de Patil et al. (2014). Se propone una nueva parametrización de la distribución skew-t de Jones y Faddy (2003) que modela mejor la asimetría. Las distribuciones son ajustadas a datos reales basados en el retorno logarítmico de la tasa de cambio de PEN a USD.<br>Tesis

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4

Muller, Fernanda Maria. "MELHORAMENTOS INFERENCIAIS NO MODELO BETA-SKEW-T-EGARCH." Universidade Federal de Santa Maria, 2016. http://repositorio.ufsm.br/handle/1/8394.

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior<br>The Beta-Skew-t-EGARCH model was recently proposed in literature to model the volatility of financial returns. The inferences over the model parameters are based on the maximum likelihood method. The maximum likelihood estimators present good asymptotic properties; however, in finite sample sizes they can be considerably biased. Monte Carlo simulations were used to evaluate the finite sample performance of point estimators. Numerical results indicated that the maximum likelihood estimators of some parameters are biased in sample si

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5

Garzon, Rozo Betty Johanna. "Modelling operational risk using skew t-copulas and Bayesian inference." Thesis, University of Edinburgh, 2016. http://hdl.handle.net/1842/25751.

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Operational risk losses are heavy tailed and are likely to be asymmetric and extremely dependent among business lines/event types. The analysis of dependence via copula models has been focussed on the bivariate case mainly. In the vast majority of instances symmetric elliptical copulas are employed to model dependence for severities. This thesis proposes a new methodology to assess, in a multivariate way, the asymmetry and extreme dependence between severities, and to calculate the capital for operational risk. This methodology simultaneously uses (i) several parametric distributions and an al

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6

Basalamah, Doaa. "Statistical Inference for a New Class of Skew t Distribution and Its Related Properties." Bowling Green State University / OhioLINK, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1496762068499547.

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Macerau, Walkiria Maria de Oliveira. "Comparação das distribuições α-estável, normal, t de student e Laplace assimétricas". Universidade Federal de São Carlos, 2012. https://repositorio.ufscar.br/handle/ufscar/4555.

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Made available in DSpace on 2016-06-02T20:06:06Z (GMT). No. of bitstreams: 1 4185.pdf: 8236823 bytes, checksum: fc450b707396aa2c496c5373af93ef3d (MD5) Previous issue date: 2012-01-27<br>Financiadora de Estudos e Projetos<br>Abstract The asymmetric distributions has experienced great development in recent times. They are used in modeling financial data, medical, genetics and other applications. Among these distributions, the Skew normal (Azzalini, 1985) has received more attention from researchers (Genton et al., (2001), Gupta et al., (2004) and Arellano-Valle et al., (2005)). We present a

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Lengua, Lafosse Patricia. "An empirical application of stochastic volatility models to Latin-American stock returns using GH skew student's t-distribution." Master's thesis, Pontificia Universidad Católica del Perú, 2015. http://tesis.pucp.edu.pe/repositorio/handle/123456789/6167.

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This paper represents empirical studies of stochastic volatility (SV) models for daily stocks returns data of a set of Latin American countries (Argentina, Brazil, Chile, Mexico and Peru) for the sample period 1996:01-2013:12. We estimate SV models incorporating both leverage effects and skewed heavy-tailed disturbances taking into account the GH Skew Student’s t-distribution using the Bayesian estimation method proposed by Nakajima and Omori (2012). A model comparison between the competing SV models with symmetric Student´s t-disturbances is provided using the log marginal likelihoods in the

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9

Hasan, Abeer. "A Study of non-central Skew t Distributions and their Applications in Data Analysis and Change Point Detection." Bowling Green State University / OhioLINK, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1371055538.

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10

Coelho, Carina Figueiredo. "Misturas finitas de normais assimétricas e de t assimétricas aplicadas em análise discriminante." Universidade Federal do Amazonas, 2013. http://tede.ufam.edu.br/handle/tede/4244.

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Submitted by Kamila Costa (kamilavasconceloscosta@gmail.com) on 2015-06-18T20:16:38Z No. of bitstreams: 1 Dissertação-Carina Figueiredo Coelho.pdf: 3096964 bytes, checksum: 57c06ccd1fdc732a7cf9a50381d3806b (MD5)<br>Approved for entry into archive by Divisão de Documentação/BC Biblioteca Central (ddbc@ufam.edu.br) on 2015-07-06T15:29:34Z (GMT) No. of bitstreams: 1 Dissertação-Carina Figueiredo Coelho.pdf: 3096964 bytes, checksum: 57c06ccd1fdc732a7cf9a50381d3806b (MD5)<br>Approved for entry into archive by Divisão de Documentação/BC Biblioteca Central (ddbc@ufam.edu.br) on 2015-07-06T15:27:26

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Lengua, Lafosse Patricia, and Gabriel Rodríguez. "An empirical application of a stochastic volatility model with GH skew Student's t -distribution to the volatility of Latin-American stock returns." Elsevier B.V, 2018. http://hdl.handle.net/10757/624614.

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El texto completo de este trabajo no está disponible en el Repositorio Académico UPC por restricciones de la casa editorial donde ha sido publicado<br>Using daily stocks returns data of a set of Latin-American countries (Argentina, Brazil, Chile, Mexico and Peru) for the sample period 1996:01–2013:12, we estimate a stochastic volatility model incorporating both leverage effects and skewed heavy-tailed disturbances through of the GH Skew Student's t-distribution based on Bayesian estimation method proposed by Nakajima and Omori (2012). Two alternative models are estimated, one using an alternat

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Kim, Young Il. "Essays on Volatility Risk, Asset Returns and Consumption-Based Asset Pricing." The Ohio State University, 2008. http://rave.ohiolink.edu/etdc/view?acc_num=osu1211912340.

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Pinheiro, Alessandra Noeli Craveiro. "Modelos de resposta ao item com função de ligação t - assimétrica." Universidade Federal de São Carlos, 2007. https://repositorio.ufscar.br/handle/ufscar/4506.

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Made available in DSpace on 2016-06-02T20:05:59Z (GMT). No. of bitstreams: 1 DissANCP.pdf: 696592 bytes, checksum: 1733e6a92a2421365932309fcb98d372 (MD5) Previous issue date: 2007-04-20<br>The Item Response Theory (IRT) is a set of mathematical models representing the probability of an individual to take a correct response of an item and its ability. The purpose of our research is to show the models formulated in the IRT under the skew-normal distributions and to develop flexible alternative models. With this goal in mind we introduced the t-skew distributions (Azzalini et al. 1999) and resu

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Silva, Diego Wesllen da. "Diagnóstico de influência bayesiano em modelos de regressão da família t-assimétrica." Universidade de São Paulo, 2017. http://www.teses.usp.br/teses/disponiveis/45/45133/tde-10082017-005536/.

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O modelo de regressão linear com erros na família de distribuições t-assimétrica, que contempla as distribuições normal, t-Student e normal assimétrica como casos particulares, tem sido considerado uma alternativa robusta ao modelo normal. Para concluir qual modelo é, de fato, mais robusto, é importante ter um método tanto para identificar uma observação como discrepante quanto aferir a influência que esta observação terá em nossas estimativas. Nos modelos de regressão bayesianos, uma das medidas de identificação de observações discrepantes mais conhecidas é a conditional predictive ordinate (

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15

Höfler, Josef [Verfasser], Donna P. [Akademischer Betreuer] Ankerst, Donna P. [Gutachter] Ankerst, and Anastasios [Gutachter] Panagiotelis. "Statistical modeling with finite mixtures of skew-t distributions and their application in the life sciences / Josef Höfler ; Gutachter: Donna P. Ankerst, Anastasios Panagiotelis ; Betreuer: Donna P. Ankerst." München : Universitätsbibliothek der TU München, 2020. http://d-nb.info/120926983X/34.

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16

Figueiredo, Cléber da Costa. "Calibração linear assimétrica." Universidade de São Paulo, 2009. http://www.teses.usp.br/teses/disponiveis/45/45133/tde-08032013-141153/.

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A presente tese aborda aspectos teóricos e aplicados da estimação dos parâmetros do modelo de calibração linear com erros distribuídos conforme a distribuição normal-assimétrica (Azzalini, 1985) e t-normal-assimétrica (Gómez, Venegas e Bolfarine, 2007). Aplicando um modelo assimétrico, não é necessário transformar as variáveis a fim de obter erros simétricos. A estimação dos parâmetros e das variâncias dos estimadores do modelo de calibração foram estudadas através da visão freqüentista e bayesiana, desenvolvendo algoritmos tipo EM e amostradores de Gibbs, respectivamente. Um dos pontos releva

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Vaičiulytė, Ingrida. "Markovo grandinės Monte-Karlo metodo tyrimas ir taikymas." Doctoral thesis, Lithuanian Academic Libraries Network (LABT), 2014. http://vddb.library.lt/obj/LT-eLABa-0001:E.02~2014~D_20141209_112429-75205.

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Disertacijoje nagrinėjami Markovo grandinės Monte-Karlo (MCMC) adaptavimo metodai, skirti efektyviems skaitiniams duomenų analizės sprendimų priėmimo su iš anksto nustatytu patikimumu algoritmams sudaryti. Suformuluoti ir išspręsti hierarchiniu būdu sudarytų daugiamačių skirstinių (asimetrinio t skirstinio, Puasono-Gauso modelio, stabiliojo simetrinio vektoriaus dėsnio) parametrų vertinimo uždaviniai. Adaptuotai MCMC procedūrai sukurti yra pritaikytas nuoseklaus Monte-Karlo imčių generavimo metodas, įvedant statistinį stabdymo kriterijų ir imties tūrio reguliavimą. Statistiniai uždaviniai išsp

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Vaičiulytė, Ingrida. "Study and application of Markov chain Monte Carlo method." Doctoral thesis, Lithuanian Academic Libraries Network (LABT), 2014. http://vddb.library.lt/obj/LT-eLABa-0001:E.02~2014~D_20141209_112440-55390.

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Markov chain Monte Carlo adaptive methods by creating computationally effective algorithms for decision-making of data analysis with the given accuracy are analyzed in this dissertation. The tasks for estimation of parameters of the multivariate distributions which are constructed in hierarchical way (skew t distribution, Poisson-Gaussian model, stable symmetric vector law) are described and solved in this research. To create the adaptive MCMC procedure, the sequential generating method is applied for Monte Carlo samples, introducing rules for statistical termination and for sample size regula

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Gomes, Priscila da Silva. "Distribuição normal assimétrica para dados de expressão gênica." Universidade Federal de São Carlos, 2009. https://repositorio.ufscar.br/handle/ufscar/4530.

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Made available in DSpace on 2016-06-02T20:06:02Z (GMT). No. of bitstreams: 1 2390.pdf: 3256865 bytes, checksum: 7ad1acbefc5f29dddbaad3f14dbcef7c (MD5) Previous issue date: 2009-04-17<br>Financiadora de Estudos e Projetos<br>Microarrays technologies are used to measure the expression levels of a large amount of genes or fragments of genes simultaneously in diferent situations. This technology is useful to determine genes that are responsible for genetic diseases. A common statistical methodology used to determine whether a gene g has evidences to diferent expression levels is the t-test which

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20

Hejblum, Boris. "Analyse intégrative de données de grande dimension appliquée à la recherche vaccinale." Thesis, Bordeaux, 2015. http://www.theses.fr/2015BORD0049/document.

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Les données d’expression génique sont reconnues comme étant de grande dimension, etnécessitant l’emploi de méthodes statistiques adaptées. Mais dans le contexte des essaisvaccinaux, d’autres mesures, comme par exemple les mesures de cytométrie en flux, sontégalement de grande dimension. De plus, ces données sont souvent mesurées de manièrelongitudinale. Ce travail est bâti sur l’idée que l’utilisation d’un maximum d’informationdisponible, en modélisant les connaissances a priori ainsi qu’en intégrant l’ensembledes différentes données disponibles, améliore l’inférence et l’interprétabilité des

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21

Matos, Gilberto da Silva. "Modelos multidimensionais da TRI com distribuições assimétricas para os traços latentes." Universidade de São Paulo, 2008. http://www.teses.usp.br/teses/disponiveis/45/45133/tde-21102009-104941/.

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A falta de alternativas ao modelo normal uni/multivariado já é um problema superado pois atualmente é possível encontrar inúmeros trabalhos que introduzem e desenvolvem generalizações da distribuição normal com relação `a assimetria, curtose e/ou multimodalidade (Branco e Arellano-Valle (2004), Genton (2004), Arellano-Valle et al. (2006)). No contexto dos modelos unidimensionais da Teoria da Resposta ao Item (TRI), Bazán (2005) percebeu esta realidade e introduziu uma classe denominada PANA (Probito Assimétrico - Normal Assimétrica) a qual permite modelar possíveis comportamentos assimétricos

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22

George, Mariam M. B. S. "Zinc regulates tolerogenic dendritic cell phenotype and skews regulatory T cell- Th17 balance." University of Cincinnati / OhioLINK, 2015. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1439305564.

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Thomason, Krista A. "Trends Analysis and a Yearly Comparison of Point Sources of Atmospheric Mercury Using HYSPLIT Back Trajectories Focused in Athens, Ohio." Ohio University / OhioLINK, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1557161272706908.

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24

Bjellerup, Mårten. "Essays on Consumption : - Aggregation, Asymmetry and Asset Distributions." Doctoral thesis, Växjö universitet, Ekonomihögskolan, EHV, 2005. http://urn.kb.se/resolve?urn=urn:nbn:se:vxu:diva-406.

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The dissertation consists of four self-contained essays on consumption. Essays 1 and 2 consider different measures of aggregate consumption, and Essays 3 and 4 consider how the distributions of income and wealth affect consumption from a macro and micro perspective, respectively. Essay 1 considers the empirical practice of seemingly interchangeable use of two measures of consumption; total consumption expenditure and consumption expenditure on nondurable goods and services. Using data from Sweden and the US in an error correction model, it is shown that consumption functions based on the two m

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Papargyris, Loukas. "Mécanismes de génération des macrophages immunorégulateurs humains : rôle de l’axe IL-27 / Adénosine / PGE2 The ecto-ATPDase CD39 is involved in the acquisition of the immunoregulatory phenotype by M-CSF-macrophages and ovarian cancer tumor-associated macrophages: Regulatory role of IL-27 Faecalibacterium prausnitzii Skews Human DC to Prime IL10-Producing T Cells Through TLR2/6/JNK Signaling and IL-10, IL-27, CD39, and IDO-1 Induction." Thesis, Angers, 2019. http://www.theses.fr/2019ANGE0038.

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Ce projet de thèse s’inscrit dans l’étude des mécanismes moléculaires associés à la polarisation des macrophages humains vers un phénotype immunorégulateur similaire à celui des macrophages tumoraux (TAM). Des données du laboratoire avaient montré le rôle de l'IL-27 dans ce processus, notamment au travers de sa capacité à moduler l'expression de CD39 qui contrôle, au moins en partie, l’acquisition d’un phénotype immunorégulateur par les macrophages humains. L’objectif de ce travail a été de préciser les mécanismes moléculaires impliqués dans l’acquisition du phénotype régulateur, en aval de l’

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Murray, Paula. "Mixtures of Skew-t Factor Analyzers." Thesis, 2012. http://hdl.handle.net/10214/5274.

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Model-based clustering allows for the identification of subgroups in a data set through the use of finite mixture models. When applied to high-dimensional microarray data, we can discover groups of genes characterized by their gene expression profiles. In this thesis, a mixture of skew-t factor analyzers is introduced for the clustering of high-dimensional data. Notably, we make use of a version of the skew-t distribution which has not previously appeared in mixture-modelling literature. Allowing a constraint on the factor loading matrix leads to two mixtures of skew-t factor analyzers mode

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Wu, Pal-Hsuan, and 吳柏璇. "The skew-t factor analysis model." Thesis, 2013. http://ndltd.ncl.edu.tw/handle/a39dwt.

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碩士<br>國立中興大學<br>統計學研究所<br>101<br>Factor analysis(FA) is a classical data reduction technique that seeks a potentially lower number of unobserved variables accounting for most correlation among the observed variables. This thesis presents an extension of the FA model by assuming jointly a restricted version of multivariate skew t distribution for the latent factors and unobservable errors, called the skew-t FA model. The proposed model shows robustness to violations of normality assumptions of the underlying latent factors and provides flexibility in capturing extra skewness as well as heavier

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Su, Yu-Chen, and 蘇育臣. "A Study of Multivariate Skew t Distribution." Thesis, 2014. http://ndltd.ncl.edu.tw/handle/69495718727163772467.

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碩士<br>國立臺北大學<br>統計學系<br>102<br>To modeling heavy-tailed and asymmetrical data, we define a new family of multivariate skew t distribution by a scale mixture of multivariate skew normal distributions. We have derived several of its probabilistic and inferential properties including explicit forms of mean vector and covariance matrix, and stochastic representation. Finally we illustrate the flexibility of this class of distributions with applications to two real data sets.

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Marchenko, Yulia V. "Multivariate Skew-t Distributions in Econometrics and Environmetrics." Thesis, 2010. http://hdl.handle.net/1969.1/ETD-TAMU-2010-12-8764.

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This dissertation is composed of three articles describing novel approaches for analysis and modeling using multivariate skew-normal and skew-t distributions in econometrics and environmetrics. In the first article we introduce the Heckman selection-t model. Sample selection arises often as a result of the partial observability of the outcome of interest in a study. In the presence of sample selection, the observed data do not represent a random sample from the population, even after controlling for explanatory variables. Heckman introduced a sample-selection model to analyze such data and pro

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Lee, Pei-Hsin, and 李沛欣. "Skew-t factor analysis models with incomplete data." Thesis, 2015. http://ndltd.ncl.edu.tw/handle/70180245396444159598.

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Lee, Han-Yang, and 李翰揚. "Application of t copula and skew t copula function in risk management." Thesis, 2015. http://ndltd.ncl.edu.tw/handle/64337841368312028910.

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Chang, Yen-Ting, and 張硯婷. "Mixtures of skew-t Factor Analyzers with Common Factor Loadings." Thesis, 2016. http://ndltd.ncl.edu.tw/handle/75061427318520687570.

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碩士<br>國立中興大學<br>統計學研究所<br>104<br>The mixture of common t factor analysis (MCtFA) model has been shown its effectiveness in robustifing the mixture of common factor analysis (MCFA) model when analyzing model-based clustering of high-dimensional data with heavy tails. However, the MCtFA model may still suffer from a lack of robustness against observations whose distributions are highly asymmetric. In this thesis, we present a further robust extension of the MCFA and MCtFA models by assuming a restricted multivariate skew-t distribution for the common factors to accommodate severe non-normal (ske

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謝宛茹. "On the mixture of skew t distributions and its applications." Thesis, 2006. http://ndltd.ncl.edu.tw/handle/85859829515591840495.

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碩士<br>國立交通大學<br>統計學研究所<br>94<br>A finite mixture model using the Student's t distribution has been recognized as a robust extension of normal mixtures. Recently, a mixture of skew normal distributions has been found to be effective in the treatment of heterogeneous data involving asymmetric behaviors across subclasses. In this article, we propose a robust mixture framework based on the skew t distribution to efficiently deal with heavy-tailedness, extra skewness and multimodality in a wide range of settings. Statistical mixture modeling based on normal, Student's t and skew normal distribution

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Ho, Hsiu-Jung, and 何秀榮. "Robust linear mixed models based on the multivariate skew t distribution." Thesis, 2010. http://ndltd.ncl.edu.tw/handle/71964987409960846029.

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博士<br>國立中興大學<br>應用數學系所<br>98<br>Linear mixed models (LMM) have been frequently used to analyze continuous longitudinal data arising particularly from a wide variety of biometrical studies. One important strength of LMM is attributed to the fact that it offers a great flexibility in modelling the between- and within-subjects correlations. In the framework of LMM, the random effects and error terms are routinely assumed to have a normal distribution due to their mathematical tractability and computational convenience. However, a serious departure of normality may suffer from lack of robustness a

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Hsu, Chia-Hui, and 徐佳慧. "Model-based clustering via mixture of skew-t distribution with missing information." Thesis, 2014. http://ndltd.ncl.edu.tw/handle/80760298934975499687.

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碩士<br>國立中興大學<br>統計學研究所<br>102<br>Multivariate mixture modeling approach using the skew-t distribution has been recently examined as a powerful and flexible tool for robust model-based clustering and classification. Missing data are a ubiquitous problem for researchers encountered in practice. In this thesis, we offer a computationally flexible EM-type procedure for maximum likelihood estimation of multivariate skew-t mixture models when missing values occur in data. Further, we present a common information-based approach to approximating the asymptotic covariance matrix of the ML estimator usi

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Tseng, Chieh-Shun, and 曾傑舜. "Mixtures of common generalized hyperbolic skew-t factor analyzers with missing information." Thesis, 2019. http://ndltd.ncl.edu.tw/cgi-bin/gs32/gsweb.cgi/login?o=dnclcdr&s=id=%22107NCHU5337002%22.&searchmode=basic.

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碩士<br>國立中興大學<br>統計學研究所<br>107<br>This paper presents a framework for maximum likelihood estimation of mixture of common generalized hyperbolic skew-t factor analyzers (MCghstFA) in the presence of missing values, which is a pervasive and practically unavoidable problem in various research areas. For computation of parameter estimates, we develop a computationally analytical expectation conditional maximization either (ECME) algorithm under a convenient multilevel hierarchical representation. We also introduced two auxiliary matrices to help us deal with missing values. Imputations of missing v

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Chen, Lianfu. "Topics on Regularization of Parameters in Multivariate Linear Regression." Thesis, 2011. http://hdl.handle.net/1969.1/ETD-TAMU-2011-12-10644.

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My dissertation mainly focuses on the regularization of parameters in the multivariate linear regression under different assumptions on the distribution of the errors. It consists of two topics where we develop iterative procedures to construct sparse estimators for both the regression coefficient and scale matrices simultaneously, and a third topic where we develop a method for testing if the skewness parameter in the skew-normal distribution is parallel to one of the eigenvectors of the scale matrix. In the first project, we propose a robust procedure for constructing a sparse estimator of

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LEE, YI FANG, and 李依芳. "Bayesian Inference of the Multiple Structural Change GARCH-type Model with Skew Student-t Er-rors." Thesis, 2019. http://ndltd.ncl.edu.tw/handle/vjb5jj.

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Pai, Hsin-Yi, and 白欣怡. "Heat-killed cells of lactobacilli skew the immune response toward T helper 1 polarization in mouse splenocytes and dendritic cell-treated T cells." Thesis, 2007. http://ndltd.ncl.edu.tw/handle/54753225007045507641.

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碩士<br>中興大學<br>食品暨應用生物科技學系<br>95<br>It is believed that probiotics play an important role for the health of the host including modulation of immune responses. Most studies have focused on the immunomodulatory effects of viable cells of lactic acid bacteria, however we investigated those of heat-killed cells of lactic acid bacteria in this study. We first observed the effects on immune functions via stimulating splenocytes with three heat-killed Lactobacillus strains. Furthermore, we also investigated the effect of mouse dendritic cells (DCs) treated with these heat-killed Lactobacillus strains

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Fesharaki, Maryam. "Mechanisms of three dimensional ocular control as revealed in patients with skew deviation." 2007. http://link.library.utoronto.ca/eir/EIRdetail.cfm?Resources__ID=452915&T=F.

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Cao, Jian. "Computation of High-Dimensional Multivariate Normal and Student-t Probabilities Based on Matrix Compression Schemes." Diss., 2020. http://hdl.handle.net/10754/662613.

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The first half of the thesis focuses on the computation of high-dimensional multivariate normal (MVN) and multivariate Student-t (MVT) probabilities. Chapter 2 generalizes the bivariate conditioning method to a d-dimensional conditioning method and combines it with a hierarchical representation of the n × n covariance matrix. The resulting two-level hierarchical-block conditioning method requires Monte Carlo simulations to be performed only in d dimensions, with d ≪ n, and allows the dominant complexity term of the algorithm to be O(n log n). Chapter 3 improves the block reordering scheme from

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