| 1. |
- Cengiz, Cigdem, et al.
(författare)
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High-dimensional profile analysis
- 2020
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Rapport (övrigt vetenskapligt/konstnärligt)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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| 2. |
- Filipiak, Katarzyna, et al.
(författare)
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Estimation under inequality constraints in univariate and multivariate linear models
- 2024
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- In this paper least squares and maximum likelihood estimates under univariate and multivariate linear models with a priori information related to maximum effects in the models are determined. Both loss functions (the least squares and negative log-likelihood) and the constraints are convex, so the convex optimization theory can be utilized to obtain estimates, which in this paper are called Safety belt estimates. In particular, the complementary slackness condition, common in convex optimization, implies two alternative types of solutions, strongly dependent on the data and the restriction.It is experimentally shown that, despite of the similarity to the ridge regression estimation under the univariate linear model, the Safety belt estimates behave usually better than estimates obtained via ridge regression. Moreover, concerning the multivariate model, the proposed technique represents a completely novel approach.
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| 3. |
- Imori, Shinpei, et al.
(författare)
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On the mean and dispersion of the Moore-Penrose generalized inverse of a Wishart matrix
- 2019
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- The Moore-Penrose inverse of a singular Wishart matrix is studied. When the scale matrix equals the identity matrix the mean and dispersion matrices of the Moore-Penrose inverse are known. When the scale matrix has an arbitrary structure no exact results are available. We complement the existing literature by deriving upper and lower bounds for the expectation and an upper bound for the dispersion of the Moore-Penrose inverse. The results show that the bounds become large when the number of rows (columns) of the Wishart matrix are close to the degrees of freedom of the distribution.
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| 4. |
- Ngailo, Edward, 1982-, et al.
(författare)
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Approximation of misclassification probabilities in linear discriminant analysis with repeated measurements
- 2020
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- In this paper, we propose approximations for the probabilities of misclassification in linear discriminant analysis when means follow a growth curve structure. The discriminant function can classify a new observation vector of p repeated measurements into one of two multivariate normal populations with equal covariance matrix. We derive certain relations of the statistics under consideration in order to obtain approximations of the misclassification errors. Finally, we perform Monte Carlo simulations to evaluate the performance of proposed results.
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| 5. |
- Ngailo, Edward, 1982-, et al.
(författare)
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Linear discriminant analysis via the Growth Curve model and restrictions on the mean space
- 2020
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- A linear classification function is applied when the means follow a Growth Curve model with restriction on the mean space. If the underlying assumption is that different groups in the experimental design follow different growth proles, a bilinear restriction on the mean space gives an Extended Growth Curve model. Given this restriction the approximations for the probability of misclassifications are derived. Moreover, a discriminant function is also derived when there exist rank restrictions on the mean parameters.
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| 6. |
- Ngaruye, Innocent, et al.
(författare)
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Small area estimation with missing data using a multivariate linear random effects model
- 2017
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- In this article small area estimation with multivariate data that follow a monotonic missing sample pattern is addressed. Random effects growth curve models with covariates are formulated. A likelihood based approach is proposed for estimation of the unknown parameters. Moreover, the prediction of random effects and predicted small area means are also discussed.
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| 7. |
- Umunoza Gasana, Emelyne, 1986-, et al.
(författare)
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Approximated misclassification errors for the likelihood based discriminant function via Edgetworth-type expansion
- 2022
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- The exact distribution of a classification function is often complicated to allow for easy numerical calculations of misclassification errors. The use of expansions is one way of dealing with this diculty. In this paper, approximate probabilities of misclassification of the maximum likelihood based discriminant function are established via an Edgeworth-type expansion based on the standard normal distribution for discriminating between two multivariate normal populations.
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| 8. |
- Umunoza Gasana, Emelyne, 1986-, et al.
(författare)
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Edgeworth-type expansion of the density of the classifier when growth curves are classified via likelihood
- 2023
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- In this paper, probabilities of misclassification of a two-step likelihood-based discriminant rule are established for the classification of growth curves. The defined two-step classifier considers the fact that the growth curves might not belong to any of the two predetermined populations. The distribution for the classifier is approximated via an Edgeworth-type expansion.
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| 9. |
- Umunoza Gasana, Emelyne, 1986-, et al.
(författare)
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Moments of the Likelihood-based Classification Function using Growth Curves
- 2023
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- The possibility that a new observation can be allocated to an unknown population is considered. von Rosen and Singull (2022) derived a classi cation rule taking into account this perspective. The classi cation rule consists of two criteria. In this paper, the mean and variance of these criteria needed to discriminate between two growth curves are established.
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| 10. |
- Umunoza Gasana, Emelyne, 1986-, et al.
(författare)
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The first two cumulants of the (quadratic) likelihood-based discriminant functions
- 2022
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- The likelihood approach used in this paper leads to quadratic discriminant functions. Classification with a known and unknown covariance matrix are separately considered, where the two cases depend on the sample size and an unknown squared Mahalanobis distance. Their exact distributions are complicated to obtain. Therefore, moments for the likelihood based discriminant functions are established to express the basic characteristics of respective distribution.
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