| 1. |
- 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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| 2. |
- 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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| 3. |
- 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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| 4. |
- Ngaruye, Innocent, et al.
(författare)
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Mean-squared errors of small area estimators under a multivariate linear model for repeated measures data
- 2017
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- In this paper, we discuss the derivation of the first and second moments for the proposed small area estimators under a multivariate linear model for repeated measures data. The aim is to use these moments to estimate the mean-squared errors (MSE) for the predicted small area means as a measure of precision. A two stage estimator of MSE is obtained. At the first stage, we derive the MSE when the covariance matrices are known. To obtain an unbiased estimator of the MSE, at the second stage, a method based on parametric bootstrap is proposed for bias correction and for prediction error that reects the uncertainty when the unknown covariance is replaced by its suitable estimator.
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| 5. |
- 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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| 6. |
- 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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| 7. |
- 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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| 8. |
- 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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| 9. |
- von Rosen, Dietrich, 1955-, et al.
(författare)
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Classification of repeated measurements using growth curves
- 2022
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- In this paper we consider discrimination between two populations of repeated measurements using growth curve models. We establish a classification procedure that is likelihood based, in that sense that we compare the two likelihoods given that the new observation belongs to respectively population. We also discuss the possibility that we classify the new observation to an unknown population, which we show is natural when considering growth curves.
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| 10. |
- Wamano, Felix, et al.
(författare)
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Estimation of trends in household living standards in Uganda using a GMANOVA-MANOVA model with rank restrictions
- 2022
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- Panel survey data from Uganda, as well as data from the 2014 Uganda Population and Housing Census data have been analysed. The Growth Curve model with rank restrictions on parameters was used to estimate the small area means.The aim of the analysis was to assess change over time in household living standards (welfare), i.e., to investigate whether households display growth in living standards? whether households grow at the same rates? and whether households in different geographical areas of the country grow at the same rates?Using a GMANOVA-MANOVA model with rank restrictions on parameters, it was established that growth in household standards of living in Uganda varied across small areas. Sub-regions (small areas) with the highest standards of living in Uganda at the endline were Central Urban region, Kampala Urban region and South Western Urban region, while the sub-regions with the lowest standards of living at the endline were North East Rural region, North East Urban region and Eastern Rural (region). The sub-regions with the highest growth rates in standards of living were Mid West Urban region, Mid North Rural region, and South Western Urban region. The sub-regions with the highest decline in standards of living were East Central Rural region, East Rural region and West Nile Urban region.
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