| 1. |
- Liang, Yuli, 1985-, et al.
(author)
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On properties of Toeplitz-type covariance matrices in models with nested random effects
- 2021
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In: Statistical papers. - : Springer. - 0932-5026 .- 1613-9798. ; 62:6, s. 2509-2528
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Journal article (peer-reviewed)abstract
- Models that capture symmetries present in the data have been widely used in different applications, with early examples from psychometric and medical research. The aim of this article is to study a random effects model focusing on the covariance structure that is block circular symmetric. Useful results are obtained for the spectra of these structured matrices.
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| 2. |
- von Rosen, Tatjana, et al.
(author)
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A new method for obtaining explicit estimators in unbalanced mixed linear models
- 2020
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In: Statistical papers. - : Springer Science and Business Media LLC. - 0932-5026 .- 1613-9798. ; 61:1, s. 371-383
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Journal article (peer-reviewed)abstract
- The general unbalanced mixed linear model with two variance components is considered. Through resampling it is demonstrated how the fixed effects can be estimated explicitly. It is shown that the obtained nonlinear estimator is unbiased and its variance is also derived. A condition is given when the proposed estimator is recommended instead of the ordinary least squares estimator.
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| 3. |
- von Rosen, Tatjana, et al.
(author)
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Bilinear regression with random effects and reduced rank restrictions
- 2020
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In: Japanese journal of statistics and data science. - : Springer Science and Business Media LLC. - 2520-8756 .- 2520-8764. ; 3:1, s. 63-72
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Journal article (peer-reviewed)abstract
- Bilinear models with three types of effects are considered: fixed effects, random effects and latent variable effects. In the literature, bilinear models with random effects and bilinear models with latent variables have been discussed but there are no results available when combining random effects and latent variables. It is shown, via appropriate vector space decompositions, how to remove the random effects so that a well-known model comprising only fixed effects and latent variables is obtained. The spaces are chosen so that the likelihood function can be factored in a convenient and interpretable way. To obtain explicit estimators, an important standardization constraint on the random effects is assumed to hold. A theorem is presented where a complete solution to the estimation problem is given.
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| 4. |
- von Rosen, Tatjana, et al.
(author)
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Small area estimation using reduced rank regression models
- 2020
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In: Communications in Statistics - Theory and Methods. - : Informa UK Limited. - 0361-0926 .- 1532-415X. ; 49:13, s. 3286-3297
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Journal article (peer-reviewed)abstract
- Small area estimation techniques have got a lot of attention during the last decades due to their important applications in survey studies. Mixed linear models and reduced rank regression analysis are jointly used when considering small area estimation. Estimates of parameters are presented as well as prediction of random effects and unobserved area measurements.
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| 5. |
- Byukusenge, Béatrice, et al.
(author)
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On an Important Residual in the GMANOVA-MANOVA Model
- 2022
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In: Journal of Statistical Theory and Practice. - : SPRINGER. - 1559-8608 .- 1559-8616. ; 16:2
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Journal article (peer-reviewed)abstract
- The main goal of this paper is to study residuals in a special case of the extended growth curve model, called the GMANOVA-MANOVA model. With the help of an example, emphasis is put on the model formulation, interpretation of the model and residuals that vanish, with a discussion about the reasons behind this fact and the consequence of it.
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| 6. |
- Byukusenge, Béatrice, 1984-, et al.
(author)
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On Residual Analysis in the GMANOVA-MANOVA Model
- 2023
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In: 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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Book chapter (peer-reviewed)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.
(author)
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On the Identification of Extreme Elements in a Residual for the GMANOVA-MANOVA Model
- 2022
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In: Innovations in Multivariate Statistical Modeling. - Cham : Springer Cham. - 9783031139710 ; , s. 119-135
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Book chapter (peer-reviewed)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-
(author)
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Residual Analysis in the GMANOVA-MANOVA Model
- 2022
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Doctoral thesis (other academic/artistic)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. |
- Cengiz, Cigdem, et al.
(author)
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High-dimensional profile analysis
- 2020
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Reports (other academic/artistic)abstract
- The three tests of profile analysis: test of parallelism, test of level and test of flatness have been studied. Likelihood ratio tests have been derived. Firstly, a traditional setting, where the sample size is greater than the dimension of the parameter space, is considered. Then, all tests have been derived in a high-dimensional setting. In high-dimensional data analysis, it is required to use some techniques to tackle the problems which arise with the dimensionality. We propose a dimension reduction method using scores which was first proposed by Läuter et al. (1996).
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| 10. |
- Cengiz, Cigdem, et al.
(author)
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Profile Analysis in High Dimensions
- 2021
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In: Journal of Statistical Theory and Practice. - : SPRINGER. - 1559-8608 .- 1559-8616. ; 15:1
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Journal article (peer-reviewed)abstract
- The three tests in profile analysis: test of parallelism, test of level and test of flatness are modified so that high-dimensional data can be analysed. Using specific scores, dimension reduction is performed and the exact null distributions are derived for the three hypotheses.
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