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- Nzabanita, Joseph, 1977-
(författare)
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Bilinear and Trilinear Regression Models with Structured Covariance Matrices
- 2015
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This thesis focuses on the problem of estimating parameters in bilinear and trilinear regression models in which random errors are normally distributed. In these models the covariance matrix has a Kronecker product structure and some factor matrices may be linearly structured. The interest of considering various structures for the covariance matrices in different statistical models is partly driven by the idea that altering the covariance structure of a parametric model alters the variances of the model’s estimated mean parameters.Firstly, the extended growth curve model with a linearly structured covariance matrix is considered. The main theme is to find explicit estimators for the mean and for the linearly structured covariance matrix. We show how to decompose the residual space, the orthogonal complement to the mean space, into appropriate orthogonal subspaces and how to derive explicit estimators of the covariance matrix from the sum of squared residuals obtained by projecting observations on those subspaces. Also an explicit estimator of the mean is derived and some properties of the proposed estimators are studied.Secondly, we study a bilinear regression model with matrix normally distributed random errors. For those models, the dispersion matrix follows a Kronecker product structure and it can be used, for example, to model data with spatio-temporal relationships. The aim is to estimate the parameters of the model when, in addition, one covariance matrix is assumed to be linearly structured. On the basis of n independent observations from a matrix normal distribution, estimating equations, a flip-flop relation, are established.At last, the models based on normally distributed random third order tensors are studied. These models are useful in analyzing 3-dimensional data arrays. In some studies the analysis is done using the tensor normal model, where the focus is on the estimation of the variance-covariance matrix which has a Kronecker structure. Little attention is paid to the structure of the mean, however, there is a potential to improve the analysis by assuming a structured mean. We formally introduce a 2-fold growth curve model by assuming a trilinear structure for the mean in the tensor normal model and propose an estimation algorithm for parameters. Also some extensions are discussed.
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- Nzabanita, Joseph
(författare)
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Estimation in Multivariate Linear Models with Linearly Structured Covariance Matrices
- 2012
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This thesis focuses on the problem of estimating parameters in multivariate linear models where particularly the mean has a bilinear structure and the covariance matrix has a linear structure. Most of techniques in statistical modeling rely on the assumption that data were generated from the normal distribution. Whereas real data may not be exactly normal, the normal distributions serve as a useful approximation to the true distribution. The modeling of normally distributed data relies heavily on the estimation of the mean and the covariance matrix. The interest of considering various structures for the covariance matrices in different statistical models is partly driven by the idea that altering the covariance structure of a parametric model alters the variances of the model’s estimated mean parameters.The extended growth curve model with two terms and a linearly structured covariance matrix is considered. In general there is no problem to estimate the covariance matrix when it is completely unknown. However, problems arise when one has to take into account that there exists a structure generated by a few number of parameters. An estimation procedure that handles linear structured covariance matrices is proposed. The idea is first to estimate the covariance matrix when it should be used to define an inner product in a regression space and thereafter reestimate it when it should be interpreted as a dispersion matrix. This idea is exploited by decomposing the residual space, the orthogonal complement to the design space, into three orthogonal subspaces. Studying residuals obtained from projections of observations on these subspaces yields explicit consistent estimators of the covariance matrix. An explicit consistent estimator of the mean is also proposed and numerical examples are given.The models based on normally distributed random matrix are also studied in this thesis. For these models, the dispersion matrix has the so called Kronecker product structure and they can be used for example to model data with spatio-temporal relationships. The aim is to estimate the parameters of the model when, in addition, one covariance matrix is assumed to be linearly structured. On the basis of n independent observations from a matrix normal distribution, estimation equations in a flip-flop relation are presented and numerical examples are given.
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- Gao, Hong, et al.
(författare)
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The landscape of tolerated genetic variation in humans and primates
- 2023
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Ingår i: Science. - : American Association for the Advancement of Science (AAAS). - 0036-8075 .- 1095-9203. ; 380:6648
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Tidskriftsartikel (refereegranskat)abstract
- Personalized genome sequencing has revealed millions of genetic differences between individuals, but our understanding of their clinical relevance remains largely incomplete. To systematically decipher the effects of human genetic variants, we obtained whole-genome sequencing data for 809 individuals from 233 primate species and identified 4.3 million common protein-altering variants with orthologs in humans. We show that these variants can be inferred to have nondeleterious effects in humans based on their presence at high allele frequencies in other primate populations. We use this resource to classify 6% of all possible human protein-altering variants as likely benign and impute the pathogenicity of the remaining 94% of variants with deep learning, achieving state-of-the-art accuracy for diagnosing pathogenic variants in patients with genetic diseases.
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- Ngaruye, Innocent
(författare)
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Contributions to Small Area Estimation : Using Random Effects Growth Curve Model
- 2017
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This dissertation considers Small Area Estimation with a main focus on estimation and prediction for repeated measures data. The demand of small area statistics is for both cross-sectional and repeated measures data. For instance, small area estimates for repeated measures data may be useful for public policy makers for different purposes such as funds allocation, new educational or health programs, etc, where decision makers might be interested in the trend of estimates for a specic characteristic of interest for a given category of the target population as a basis of their planning.It has been shown that the multivariate approach for model-based methods in small area estimation may achieve substantial improvement over the usual univariate approach. In this work, we consider repeated surveys taken on the same subjects at different time points. The population from which a sample has been drawn is partitioned into several non-overlapping subpopulations and within all subpopulations there is the same number of group units. The aim is to propose a model that borrows strength across small areas and over time with a particular interest of growth profiles over time. The model accounts for repeated surveys, group individuals and random effects variations.Firstly, a multivariate linear model for repeated measures data is formulated under small area estimation settings. The estimation of model parameters is discussed within a likelihood based approach, the prediction of random effects and the prediction of small area means across timepoints, per group units and for all time points are obtained. In particular, as an application of the proposed model, an empirical study is conducted to produce district level estimates of beans in Rwanda during agricultural seasons 2014 which comprise two varieties, bush beans and climbing beans.Secondly, the thesis develops the properties of the proposed estimators and discusses the computation of their first and second moments. Through a method based on parametric bootstrap, these moments are used to estimate the mean-squared errors for the predicted small area means. Finally, a particular case of incomplete multivariate repeated measures data that follow a monotonic sample pattern for small area estimation is studied. By using a conditional likelihood based approach, the estimators of model parameters are derived. The prediction of random effects and predicted small area means are also produced.
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- Ngaruye, Innocent
(författare)
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Small Area Estimation for Multivariate Repeated Measures Data
- 2014
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This thesis considers Small Area Estimation with a main focus on estimation and prediction theory for repeated measures data. The demand for small area statistics is for both cross-sectional and repeated measures data. For instance, small area estimates for repeated measures data may be used by public policy makers for different purposes such as funds allocation, new educational or health programs and in some cases, they might be interested in a given group of population.It has been shown that the multivariate approach for model-based methods in small area estimation may achieve substantial improvement over the usual univariate approach. In this work, we consider repeated surveys including the same subjects at different time points. The population from which a sample has been drawn is partitioned into several subpopulations and within all subpopulations there is the same number of group units. For this setting a multivariate linear regression model is formulated. The aim of the proposed model is to borrow strength across small areas and over time with a particular interest of growth profiles over time. The model accounts for repeated surveys, group individuals and random effects variations.The estimation of model parameters is discussed with a restricted maximum likelihood based approach. The prediction of random effects and the prediction of small area means across time points, per group units and for all time points are derived. The theoretical results have also been supported by a simulation study and finally, suggestions for future research are presented.
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- Nordquist, Niklas
(författare)
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Genetic Studies of Rheumatoid Arthritis using Animal Models
- 2001
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Predisposition to autoimmune diseases such as, rheumatoid arthritis, diabetes, and multiple sclerosis, is caused by the effect of multiple genes and a strong influence from the environment. In this study, I have investigated genetic factors that confer susceptibility to rheumatoid arthritis in a rat model. This work has led to the identification of several chromosomal regions, containing uncharacterized genes that directly or indirectly are associated to the arthritis development in these rats. We have observed that timing, gender, and genetic interactions are features that play a part in the effect that these genetic factors exert. Unarguably, animal models for human disorders display differences to the human form of disease. An important fact is however that the same chromosomal regions are identified in both rodent and human studies, which suggests that there are genetic factors that we have in common, which are involved directly or indirectly with an autoimmune response. Focusing the interest on these similarities, and on the possibility to apply a wide set of genetic tools, make animal models an invaluable, and probably necessary, instrument to dissect the genetic component of complex disorders. To fully comprehend the genetic basis for a complex disorder like this, will require understanding of how multiple genes interact with each other to cause disease. We have been able to demonstrate that chronic arthritis, in a rat model for rheumatoid arthritis, is regulated by several genes and that these act during different temporal phases of the disease. These findings will hopefully contribute to our understanding of the etiology and progression of rheumatoid arthritis.
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- Pielaszkiewicz, Jolanta Maria
(författare)
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Contributions to High–Dimensional Analysis under Kolmogorov Condition
- 2015
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This thesis is about high–dimensional problems considered under the so{called Kolmogorov condition. Hence, we consider research questions related to random matrices with p rows (corresponding to the parameters) and n columns (corresponding to the sample size), where p > n, assuming that the ratio converges when the number of parameters and the sample size increase.We focus on the eigenvalue distribution of the considered matrices, since it is a well–known information–carrying object. The spectral distribution with compact support is fully characterized by its moments, i.e., by the normalized expectation of the trace of powers of the matrices. Moreover, such an expectation can be seen as a free moment in the non–commutative space of random matrices of size p x p equipped with the functional . Here, the connections with free probability theory arise. In the relation to that eld we investigate the closed form of the asymptotic spectral distribution for the sum of the quadratic forms. Moreover, we put a free cumulant–moment relation formula that is based on the summation over partitions of the number. This formula is an alternative to the free cumulant{moment relation given through non{crossing partitions ofthe set.Furthermore, we investigate the normalized and derive, using the dierentiation with respect to some symmetric matrix, a recursive formula for that expectation. That allows us to re–establish moments of the Marcenko–Pastur distribution, and hence the recursive relation for the Catalan numbers.In this thesis we also prove that the , where , is a consistent estimator of the . We consider,where , which is proven to be normally distributed. Moreover, we propose, based on these random variables, a test for the identity of the covariance matrix using a goodness{of{t approach. The test performs very well regarding the power of the test compared to some presented alternatives for both the high–dimensional data (p > n) and the multivariate data (p ≤ n).
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- Tovesson, Fredrik, 1975-
(författare)
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The neutron-induced fission cross section of 233Pa : and the quest for clean and safe nuclear energy
- 2003
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Neutron-induced fission of 233Pa has been investigated between 1.0 and 8.5 MeV, and the reaction cross section was determined. Due to the short half-life of 233Pa for β-decay, fission events from the daughter product 233U affect the analysis of the protactinium experiment. In order to be able to correct for this contamination by ingrowing 233U, its fission cross section was measured as well in the same energy region.The result for the 233Pa(n,f) cross section is compared with previous theoretical evaluations and indirect cross section estimations extracted from fission probability data. The cross section data that were measured in this work are lower than all other values for this isotope. The 233U(n,f) cross section values are also compared to evaluations. The evaluations for the neutron-induced fission cross section of 233U(n,f) are based on a large set of experimental values, and are thus considered to be very accurate. A good agreement between the results obtained in this work and the evaluations is observed in this case.New model calculations, based on the statistical model for nuclear reactions, are compared to the experimental results for the 233Pa(n,f) cross section. These theoretical calculations describe the experimental results very accurately, and can be used to extract information about the fissioning system.The main motivation for this work is its relevance for the thorium-based nuclear fuel cycle, which has been proposed for advanced reactor facilities intended for safe power supply and transmutation of nuclear waste.
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