| 1. |
- 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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| 2. |
- Nzabanita, Joseph, 1977-, et al.
(författare)
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Estimation of parameters in the extended growth curve model with a linearly structured covariance matrix
- 2012
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Ingår i: Acta et Commentationes Universitatis Tartuensis de Mathematica. - 1406-2283 .- 2228-4699. ; 16:1, s. 13-32
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Tidskriftsartikel (refereegranskat)abstract
- In this paper the extended growth curve model with two terms and a linearly structured covariance matrix is considered. We propose an estimation procedure that handles linear structured covariance matrices. 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.
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| 3. |
- Ohlson, Martin, 1977-, et al.
(författare)
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More on the Kronecker Structured Covariance Matrix
- 2012
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Ingår i: Communications in Statistics - Theory and Methods. - : Taylor & Francis. - 0361-0926 .- 1532-415X. ; 41:13-14, s. 2512-2523
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, the multivariate normal distribution with a Kronecker product structured covariance matrix is studied. Particularly focused is the estimation of a Kronecker structured covariance matrix of order three, the so called double separable covariance matrix. The suggested estimation generalizes the procedure proposed by Srivastava et al. (2008) for a separable covariance matrix. The restrictions imposed by separability and double separability are also discussed.
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| 4. |
- Singull, Martin, 1977-, et al.
(författare)
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On the Distribution of Matrix Quadratic Forms
- 2012
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Ingår i: Communications in Statistics - Theory and Methods. - : Informa UK Limited. - 0361-0926 .- 1532-415X. ; 41:18, s. 3403-3415
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Tidskriftsartikel (refereegranskat)abstract
- A characterization of the distribution of the multivariate quadratic form given by XAX', where X is a p x n normally distributed matrix and A is an n x n symmetric real matrix, is presented. We show that the distribution of the quadratic form is the same as the distribution of a weighted sum of non central Wishart distributed matrices. This is applied to derive the distribution of the sample covariance between the rows of X when the expectation is the same for every column and is estimated with the regular mean.
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| 5. |
- Ahmad, M. Rauf, et al.
(författare)
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A note on mean testing for high dimensional multivariate data under non-normality
- 2013
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Ingår i: Statistica Neerlandica. - : Wiley. - 0039-0402 .- 1467-9574. ; 67:1, s. 81-99
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Tidskriftsartikel (refereegranskat)abstract
- A test statistic is considered for testing a hypothesis for the mean vector for multivariate data, when the dimension of the vector, p, may exceed the number of vectors, n, and the underlying distribution need not necessarily be normal. With n,p?8, and under mild assumptions, but without assuming any relationship between n and p, the statistic is shown to asymptotically follow a chi-square distribution. A by product of the paper is the approximate distribution of a quadratic form, based on the reformulation of the well-known Box's approximation, under high-dimensional set up. Using a classical limit theorem, the approximation is further extended to an asymptotic normal limit under the same high dimensional set up. The simulation results, generated under different parameter settings, are used to show the accuracy of the approximation for moderate n and large p.
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| 6. |
- Byukusenge, Béatrice, 1984-, et al.
(författare)
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On Residual Analysis in the GMANOVA-MANOVA Model
- 2023
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Ingår i: Trends in Mathematical, Information and Data Sciences: A Tribute to Leandro Pardo. - Cham : Springer International Publishing. - 9783031041365 - 9783031041372 ; , s. 287-305
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Bokkapitel (refereegranskat)abstract
- In this article, the GMANOVA-MANOVA model is considered. Two different matrix residuals are established. The interpretation of the residuals is discussed and several properties are verified. A data set illustrates how the residuals can be used.
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| 7. |
- Byukusenge, Béatrice, 1984-, et al.
(författare)
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On the Identification of Extreme Elements in a Residual for the GMANOVA-MANOVA Model
- 2022
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Ingår i: Innovations in Multivariate Statistical Modeling. - Cham : Springer Cham. - 9783031139710 ; , s. 119-135
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Bokkapitel (refereegranskat)abstract
- Two different matrix residuals in a special GMANOVA-MANOVA model have previously been established (see Byukusenge et al., 2021, “On residual analysis in the GMANOVA-MANOVA model”). The residual that is studied in this article is constructed via the difference of the observed group means and the estimated mean structure. The residual provides information about the appropriateness of the model assumptions concerning the mean structure. The aim of this paper is to study the distribution of the largest elements (by absolute value) of the residual via two data sets. Parametric bootstrap is used to identify thresholds so that extreme elements of the residuals can be identified.
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| 8. |
- Byukusenge, Béatrice, 1984-
(författare)
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Residual Analysis in the GMANOVA-MANOVA Model
- 2022
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This thesis focuses on the establishment and analysis of residuals in the so called GMANOVA-MANOVA model. The model is a special case of the Extended Growth Curve Model. It has two terms where one term models the profiles (growth curves) and the other the covariables of interest. This model is useful in studying growth curves in short time series in fields such as economics, biology, medicine, and epidemiology. Furthermore, in the literature, residuals have been extensively studied and used to check model adequacy in univariate linear models. This thesis contributes to the extension of the study of residuals in the GMANOVA-MANOVA model. In this thesis, a new pair of residuals is established via the maximum likelihood estimators of the parameters in the model. One residual indicates whether an individual is far away from the group means and a second residual is used to check assumptions about the mean structure. Different properties of these residuals are verified and their interpretation is discussed. Moreover, using parametric bootstrap, the empirical distributions of the extreme elements in the residuals are derived. Finally, testing bilinear restriction in the MANOVA model is considered. One can show that the MANOVA model with bilinear restrictions is nothing more than a GMANOVA-MANOVA model. Furthermore, the likelihood ratio test can be shown to be given as a function of the residuals to the GMANOVA-MANOVA model, which can be used to understand the appropriateness of the model and test the bilinear hypothesis.
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| 9. |
- Börjesson, Lukas, et al.
(författare)
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Forecasting Financial Time Series through Causal and Dilated Convolutional Neural Networks
- 2020
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Ingår i: Entropy. - : MDPI. - 1099-4300. ; 22:10
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, predictions of future price movements of a major American stock index were made by analyzing past movements of the same and other correlated indices. A model that has shown very good results in audio and speech generation was modified to suit the analysis of financial data and was then compared to a base model, restricted by assumptions made for an efficient market. The performance of any model, trained by looking at past observations, is heavily influenced by how the division of the data into train, validation and test sets is made. This is further exaggerated by the temporal structure of the financial data, which means that the causal relationship between the predictors and the response is dependent on time. The complexity of the financial system further increases the struggle to make accurate predictions, but the model suggested here was still able to outperform the naive base model by more than 20% and 37%, respectively, when predicting the next day’s closing price and the next day’s trend.
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| 10. |
- Coelho, Carlos A., et al.
(författare)
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Testing for double complete symmetry
- 2020
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Ingår i: Recent Developments in Multivariate and Random Matrix Analysis. - Cham : Springer Cham. - 9783030567729 - 9783030567736 ; , s. 17-39
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Bokkapitel (refereegranskat)abstract
- In this paper the authors take an approach over the likelihood ratio test for double complete symmetry, which enables a particularly simple implementation of the test as well as a particularly adequate way towards obtaining very sharp approximations for the exact distribution of the test statistic. Numerical studies show the very good performance of the near-exact distributions derived, namely their very good performance for very small sample sizes and their asymptotic behavior for increasing numbers of variables involved.
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