| 1. |
- Bauder, David, et al.
(författare)
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Bayesian estimation of the efficient frontier
- 2019
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Ingår i: Scandinavian Journal of Statistics. - : Wiley. - 0303-6898 .- 1467-9469. ; 46:3, s. 802-830
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, we consider the estimation of the three determining parameters of the efficient frontier, the expected return, and the variance of the global minimum variance portfolio and the slope parameter, from a Bayesian perspective. Their posterior distribution is derived by assigning the diffuse and the conjugate priors to the mean vector and the covariance matrix of the asset returns and is presented in terms of a stochastic representation. Furthermore, Bayesian estimates together with the standard uncertainties for all three parameters are provided, and their asymptotic distributions are established. All obtained findings are applied to real data, consisting of the returns on assets included into the S&P 500. The empirical properties of the efficient frontier are then examined in detail.
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| 2. |
- Bodnar, Olha, senior lecturer, 1979-, et al.
(författare)
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Bayesian estimation in multivariate inter-laboratory studies with unknown covariance matrices
- 2023
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Ingår i: Metrologia. - : IOP Publishing Ltd. - 0026-1394 .- 1681-7575. ; 60:5
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Tidskriftsartikel (refereegranskat)abstract
- In the paper we present Bayesian inference procedures for the parameters of multivariate random effects model, which is used as a quantitative tool for performing multivariate key comparisons and multivariate inter-laboratory studies. The developed new approach does not require that the reported covariance matrices of participating laboratories are known and, as such, it can be used when they are estimated from the measurement results. The Bayesian inference procedures are based on samples generated from the derived posterior distribution when the Berger and Bernardo reference prior and the Jeffreys prior are assigned to the model parameter. Three numerical algorithms for the construction of Markov chains are provided and implemented in the CCAUV.V-K1 key comparisons. All three approaches yield similar Bayesian estimators with wider credible intervals when the Berger and Bernardo reference prior is used. Also, the Bayesian estimators for the elements of the inter-laboratory covariance matrix are larger under this prior than for the Jeffreys prior. Finally, the constructed joint credible sets for the components of the overall mean vector indicate the presence of linear dependence between them which cannot be captured when only univariate key comparisons are performed.
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| 3. |
- Bodnar, Olha, senior lecturer, 1979-, et al.
(författare)
-
Bayesian estimation in multivariate inter-laboratory studies with unknown covariance matrices
- 2023
-
Ingår i: Metrologia. - : IOP Publishing Ltd. - 0026-1394 .- 1681-7575. ; 60:5
-
Tidskriftsartikel (refereegranskat)abstract
- In the paper we present Bayesian inference procedures for the parameters of multivariate random effects model, which is used as a quantitative tool for performing multivariate key comparisons and multivariate inter-laboratory studies. The developed new approach does not require that the reported covariance matrices of participating laboratories are known and, as such, it can be used when they are estimated from the measurement results. The Bayesian inference procedures are based on samples generated from the derived posterior distribution when the Berger and Bernardo reference prior and the Jeffreys prior are assigned to the model parameter. Three numerical algorithms for the construction of Markov chains are provided and implemented in the CCAUV.V-K1 key comparisons. All three approaches yield similar Bayesian estimators with wider credible intervals when the Berger and Bernardo reference prior is used. Also, the Bayesian estimators for the elements of the inter-laboratory covariance matrix are larger under this prior than for the Jeffreys prior. Finally, the constructed joint credible sets for the components of the overall mean vector indicate the presence of linear dependence between them which cannot be captured when only univariate key comparisons are performed.
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| 4. |
- Bodnar, Olha, senior lecturer, 1979-, et al.
(författare)
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Constructing Bayesian tangency portfolios under short-selling restrictions
- 2024
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Ingår i: Finance Research Letters. - : Elsevier. - 1544-6123 .- 1544-6131. ; 62
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Tidskriftsartikel (refereegranskat)abstract
- We address the challenge of constructing tangency portfolios in the context of short-selling restrictions. Utilizing Bayesian techniques, we reparameterize the asset return model, enabling direct determination of priors for the tangency portfolio weights. This facilitates the integration of non-negative weight constraints into an investor's prior beliefs, resulting in a posterior distribution focused exclusively on non-negative values. Portfolio weight estimators are subsequently derived via the Markov Chain Monte Carlo (MCMC) methodology. Our novel Bayesian approach is empirically illustrated using the most significant stocks in the S&P 500 index. The method showcases promising results in terms of risk-adjusted returns and interpretability.
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| 5. |
- Bodnar, Olha, senior lecturer, 1979-, et al.
(författare)
-
Constructing Bayesian tangency portfolios under short-selling restrictions
- 2024
-
Ingår i: Finance Research Letters. - : Elsevier. - 1544-6123 .- 1544-6131. ; 62
-
Tidskriftsartikel (refereegranskat)abstract
- We address the challenge of constructing tangency portfolios in the context of short-selling restrictions. Utilizing Bayesian techniques, we reparameterize the asset return model, enabling direct determination of priors for the tangency portfolio weights. This facilitates the integration of non-negative weight constraints into an investor’s prior beliefs, resulting in a posterior distribution focused exclusively on non-negative values. Portfolio weight estimators are subsequently derived via the Markov Chain Monte Carlo (MCMC) methodology. Our novel Bayesian approach is empirically illustrated using the most significant stocks in the S&P 500 index. The method showcases promising results in terms of risk-adjusted returns and interpretability.
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| 6. |
- Bodnar, Olha, senior lecturer, 1979-, et al.
(författare)
-
Objective Bayesian Meta-Analysis Based on Generalized Marginal Multivariate Random Effects Model
- 2024
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Ingår i: Bayesian Analysis. - : International Society for Bayesian Analysis. - 1936-0975 .- 1931-6690. ; 19:2, s. 531-564
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Tidskriftsartikel (refereegranskat)abstract
- Objective Bayesian inference procedures are derived for the parameters of the multivariate random effects model generalized to elliptically contoured distributions. The posterior for the overall mean vector and the between-study covariance matrix is deduced by assigning two noninformative priors to the model parameter, namely the Berger and Bernardo reference prior and the Jeffreys prior, whose analytical expressions are obtained under weak distributional assumptions. It is shown that the only condition needed for the posterior to be proper is that the sample size is larger than the dimension of the data-generating model, inde-pendently of the class of elliptically contoured distributions used in the definition of the generalized multivariate random effects model. The theoretical findings of the paper are applied to real data consisting of ten studies about the effectiveness of hypertension treatment for reducing blood pressure where the treatment effects on both the systolic blood pressure and diastolic blood pressure are investigated.
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| 7. |
- Bodnar, Olha, et al.
(författare)
-
Objective Bayesian Meta-Analysis Based on Generalized Marginal Multivariate Random Effects Model
- 2024
-
Ingår i: Bayesian Analysis. - 1936-0975 .- 1931-6690. ; 19:2, s. 531-564
-
Tidskriftsartikel (refereegranskat)abstract
- Objective Bayesian inference procedures are derived for the parameters of the multivariate random effects model generalized to elliptically contoured distributions. The posterior for the overall mean vector and the between -study covariance matrix is deduced by assigning two noninformative priors to the model parameter, namely the Berger and Bernardo reference prior and the Jeffreys prior, whose analytical expressions are obtained under weak distributional assumptions. It is shown that the only condition needed for the posterior to be proper is that the sample size is larger than the dimension of the data -generating model, independently of the class of elliptically contoured distributions used in the definition of the generalized multivariate random effects model. The theoretical findings of the paper are applied to real data consisting of ten studies about the effectiveness of hypertension treatment for reducing blood pressure where the treatment effects on both the systolic blood pressure and diastolic blood pressure are investigated. MSC2020 subject classifications: Primary 62F15, 62H10; secondary 62H12.
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| 8. |
- Bodnar, Olga, et al.
(författare)
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Practical aspects of Bayesian multivariate meta-analysis : [Практичні аспекти Байєсівського багатовимірного мета-аналізу]
- 2022
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Ingår i: Ukrainian Metrological Journal. - : National Scientific Centre Institute of Metrology. - 2306-7039 .- 2522-1345. ; 2022:4, s. 7-11
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Tidskriftsartikel (refereegranskat)abstract
- Multivariate meta-analysis is a mostly used approach when multivariate results of several studies are pooled together. The multivariate model of random effects provides a tool to perform the multivariate meta-analysis in practice. In this paper, we discuss Bayesian inference procedures derived for the multivariate model of random effects when the model parameters are endowed with two non-informative priors: the Berger-Bernardo reference prior and the Jeffreys prior. Moreover, two Metropolis-Hastings algorithms are presented, and their convergence properties are analysed via simulations.
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| 9. |
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| 10. |
- Bodnar, Olha, senior lecturer, 1979-, et al.
(författare)
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Recent advances in shrinkage-based high-dimensional inference
- 2022
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Ingår i: Journal of Multivariate Analysis. - : Elsevier. - 0047-259X .- 1095-7243. ; 188
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Tidskriftsartikel (refereegranskat)abstract
- Recently, the shrinkage approach has increased its popularity in theoretical and applied statistics, especially, when point estimators for high-dimensional quantities have to be constructed. A shrinkage estimator is usually obtained by shrinking the sample estimator towards a deterministic target. This allows to reduce the high volatility that is commonly present in the sample estimator by introducing a bias such that the mean-square error of the shrinkage estimator becomes smaller than the one of the corresponding sample estimator. The procedure has shown great advantages especially in the high-dimensional problems where, in general case, the sample estimators are not consistent without imposing structural assumptions on model parameters.In this paper, we review the mostly used shrinkage estimators for the mean vector, covariance and precision matrices. The application in portfolio theory is provided where the weights of optimal portfolios are usually determined as functions of the mean vector and covariance matrix. Furthermore, a test theory on the mean-variance optimality of a given portfolio based on the shrinkage approach is presented as well.
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