| 1. |
- Dushimirimana, Justine, et al.
(författare)
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Growth curve model for analyzing the effects of Calcium foliar feed on the wilting rate of post-harvest rose flowers
- 2021
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Ingår i: African Journal of Applied Statistics. - : The Statistics and Probability African Society. - 2316-0861. ; 8:2, s. 1181-1197
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Tidskriftsartikel (refereegranskat)abstract
- Cut rose flowers contribute to the economy and development of the export markets for several developing countries. Despite this contribution, profitable production of rose flowers is limited by wilting which leads to lower production. This paper aims to investigate the effects of Calcium foliar feed on the wilting rate of post-harvest rose flowers using the Growth Curve Model. This method was applied to the data consisting of wilting scores on five treatment groups. The Likelihood ratio test was used to test the growth curve and the equality of the growth curves in all groups. Results revealed that the expected growth curves for all groups followed different quadratic functions. The results also revealed that the wilting rate increased with the increase of calcium concentration compared to the control. This leads to a useful model for policy-makers or further analyses.
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| 2. |
- Habyarimana, Cassien, et al.
(författare)
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Estimation of Parameters in the Growth Curve Model with a Linearly Structured Covariance Matrix : A Simulation Study
- 2017
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Ingår i: International Journal of Scientific Engineering and Technology. - 2277-1581. ; 6:1, s. 45-49
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, the implementation of algorithm proposed in (Nzabanita, J., et al. 2012) for some known linear structures on the covariance matrix Σ is performed and simulations for different sample sizes are repeated many times. For these simulations, the percentages of non positive definite estimates are produced, and the linear structures are identified and classified.
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| 3. |
- Muhmuza, Rebecca Nalule, et al.
(författare)
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Determining influential factors in spatio-temporal models
- 2019
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Ingår i: Proceedings of 18th Applied Stochastic Models and Data Analysis International Conference with the Demographics 2019 Workshop, Florence, Italy: 11-14 June, 2019. - : ISAST: International Society for the Advancement of Science and Technology. - 9786185180331 ; , s. 547-558
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Konferensbidrag (refereegranskat)abstract
- In various areas of modern statistical applications such as in Environmetrics, Image Processing, Epidemiology, Biology, Astronomy, Industrial Mathematics, and many others, we encounter challenges of analyzing massive data sets which are spatially observable, often presented as maps, and temporally correlated. The analysis of such data is usually performed with the goal to obtain both the spatial interpolation and the temporal prediction. In both cases, the data-generating process has to be fitted by an appropriate stochastic model which should have two main properties: (i) it should provide a good fit to the true underlying model; (ii) its structure could not be too complicated avoiding considerable estimation error appeared by fitting the model to real data. Consequently, achieving the reasonable trade-off between the model uncertainty and the parameter uncertainty is one of the most difficult questions of modern statistical theory.We deal with this problem in the case of general spatio-temporal models by applying the LOESS predictor for both the spatial interpolation and the temporal prediction. The number of closest neighboring regions to be used in its construction is determined by cross-validation. We also discuss the computational aspects in the case of large-dimensional data and apply the theoretical findings to real data consisting of the number of influenza cases observed in the south of Germany.
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| 4. |
- Nalule Muhumuza, Rebecca, et al.
(författare)
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Determining Influential Factors in Spatio-temporal Models
- 2020
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Ingår i: Demography of Population Health, Aging and Health Expenditures. - Cham : Springer International Publishing. - 9783030446956 - 9783030446949 ; , s. 347-357
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Bokkapitel (refereegranskat)abstract
- In various areas of modern statistical applications such as in Environmetrics, Image Processing, Epidemiology, Biology, Astronomy, Industrial Mathematics, and many others, we encounter challenges of analyzing massive data sets which are spatially observable, often presented as maps, and temporally correlated. The analysis of such data is usually performed with the goal to obtain both the spatial interpolation and the temporal prediction. In both cases, the data-generating process has to be fitted by an appropriate stochastic model which should have two main properties: (i) it should provide a good fit to the true underlying model; (ii) its structure could not be too complicated avoiding considerable estimation error that appears by fitting the model to real data. Consequently, achieving the reasonable trade-off between the model uncertainty and the parameter uncertainty is one of the most difficult questions of modern statistical theory.We deal with this problem in the case of general spatio-temporal models by applying the LOESS predictor for both the spatial interpolation and the temporal prediction. The number of closest neighboring regions to be used in its construction is determined by cross-validation. We also discuss the computational aspects in the case of large-dimensional data and apply the theoretical findings to real data consisting of the number of influenza cases observed in the south of Germany.
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| 5. |
- Ngaruye, Innocent, et al.
(författare)
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Small Area Estimation under a Multivariate Linear Model for Repeated Measures Data
- 2015
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- In this paper, we consider small area estimation under a multivariate linear regression model for repeated measures data. The aim of the proposed model is to get a model which borrows strength across small areas and over time, by incorporating simultaneously the area effects and time correlation. The model accounts for repeated surveys, group individuals and random effects variations. Estimation of model parameters is discussed within a restricted maximum likelihood based approach. Prediction of random e ects and the prediction of small area means across time points and per group units for all time points are derived. The results are supported by a simulation study.
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| 6. |
- Ngaruye, Innocent, et al.
(författare)
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Small Area Estimation under a Multivariate Linear Model for Repeated measures Data
- 2017
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Ingår i: Communications in Statistics - Theory and Methods. - New York : Taylor & Francis. - 0361-0926 .- 1532-415X. ; 46:21, s. 10835-10850
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Tidskriftsartikel (refereegranskat)abstract
- In this article, Small Area Estimation under a Multivariate Linear model for repeated measures data is considered. The proposed model aims to get a model which borrows strength both across small areas and over time. The model accounts for repeated surveys, grouped response units and random effects variations. Estimation of model parameters is discussed within a likelihood based approach. Prediction of random effects, small area means across time points and per group units are derived. A parametric bootstrap method is proposed for estimating the mean squared error of the predicted small area means. Results are supported by a simulation study.
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| 7. |
- 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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| 8. |
- Nzabanita, Joseph, et al.
(författare)
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Bilinear regression model with Kronecker and linear structures for the covariance matrix
- 2015
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Ingår i: Afrika Statistika. - : Statistics and Probability African Society (SPAS). - 2316-090X. ; 10:2, s. 827-837
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, the bilinear regression model based on normally distributed random matrix is studied. 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, estimating equations in a flip-flop relation are established and the consistency of estimators is studied.
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| 9. |
- Nzabanita, Joseph, 1977-, et al.
(författare)
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Estimation in multivariate linear models with Kronecker product and linear structures on the covariance matrices
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Annan publikation (övrigt vetenskapligt/konstnärligt)abstract
- This paper deals with models based on normally distributed random matrices. More specifically the model considered is X ∼ Np,q(M, Σ, Ψ) with mean M, a p×q matrix, assumed to follow a bilinear structure, i.e., E[X] = M = ABC, where A and C are known design matrices, B is unkown parameter matrix, and the dispersion matrix of X has a Kronecker product structure, i.e., D[X] = Ψ ⊗ Σ, where both Ψ and Σ are unknown positive definite matrices. The model may be used for example to model data with spatiotemporal relationships. The aim is to estimate the parameters of the model when, in addition, Σ is assumed to be linearly structured. In the paper, on the basis of n independent observations on the random matrix X, estimation equations in a flip-flop relation are presented and numerical examples are given.
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| 10. |
- 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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