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N. Parolya

33 records found

This paper is concerned with deriving a new test on a covariance matrix which is based on its nonlinear shrinkage estimator. The distribution of the test statistic is deduced under the null hypothesis in the large-dimensional setting, that is, when p/n tend to some positive const ...
In this paper, we analyze the asymptotic behavior of the main characteristics of the mean-variance efficient frontier employing random matrix theory. Our particular interest covers the case when the dimension p and the sample size n tend to infinity simultaneously and their ratio ...
This paper discusses the practical aspects of working with high-dimensional shrinkage portfolios. It presents the R package HDShOP which provides a comprehensive framework for such work. In particular, we cover the construction of portfolios using shrinkage-based estimators for t ...
Consider a random vector y = Σ 1/2 x, where the p elements of the vector x are i.i.d. real-valued random variables with zero mean and finite fourth moment, and Σ 1/2 is a deterministic p × p matrix such that the eigenvalues of the ...
The chapter is concerned with finding the asymptotic distribution of the estimated shrinkage intensity used in the definition of the linear shrinkage estimator of the covariance matrix, derived by Bodnar et al. (J Multivar Anal 132:215–228, 2014). As a result, a new test statisti ...
In this paper, we show the central limit theorem for the logarithmic determinant of the sample correlation matrix R constructed from the (p × n)-dimensional data matrix X containing independent and identically distributed random entries with mean zero, variance one and infinite f ...
In this paper, we derive an analytical solution to the dynamic optimal portfolio choice problem in the case of an investor equipped with a power utility function of wealth. The results are established by solving the Bellman backward recursion under the assumption that the vector ...

Predicting Beta-Lactam Target Non-Attainment in ICU Patients at Treatment Initiation

Development and External Validation of Three Novel (Machine Learning) Models

In the intensive care unit (ICU), infection-related mortality is high. Although adequate antibiotic treatment is essential in infections, beta-lactam target non-attainment occurs in up to 45% of ICU patients, which is associated with a lower likelihood of clinical success. To opt ...
In this paper, new results in random matrix theory are derived, which allow us to construct a shrinkage estimator of the global minimum variance (GMV) portfolio when the shrinkage target is a random object. More specifically, the shrinkage target is determined as the holding port ...
The main contribution of this paper is the derivation of the asymptotic behavior of the out-of-sample variance, the out-of-sample relative loss, and of their empirical counterparts in the high-dimensional setting, i.e., when both ratios p/n and p/m tend to some positive constants ...
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 det ...
In this paper, using the shrinkage-based approach for portfolio weights and modern results from random matrix theory we construct an effective procedure for testing the efficiency of the expected utility (EU) portfolio and discuss the asymptotic behavior of the proposed test stat ...
Optimal portfolio selection problems are determined by the (unknown) parameters of the data generating process. If an investor wants to realize the position suggested by the optimal portfolios, he/she needs to estimate the unknown parameters and to account for the parameter uncer ...
In this article, we estimate the mean-variance portfolio in the high-dimensional case using the recent results from the theory of random matrices. We construct a linear shrinkage estimator which is distribution-free and is optimal in the sense of maximizing with probability one t ...
We derive new results related to the portfolio choice problem for power and logarithmic utilities. Assuming that the portfolio returns follow an approximate log-normal distribution, the closed-form expressions of the optimal portfolio weights are obtained for both utility functio ...
We consider the estimation of the multi-period optimal portfolio obtained by maximizing an exponential utility. Employing the Jeffreys non-informative prior and the conjugate informative prior, we derive stochastic representations for the optimal portfolio weights at each time po ...
A reflexive generalized inverse and the Moore-Penrose inverse are often confused in statistical literature but in fact they have completely different behaviour in case the population covariance matrix is not a multiple of identity. In this paper, we study the spectral properties ...

Bayesian mean–variance analysis

Optimal portfolio selection under parameter uncertainty

The paper solves the problem of optimal portfolio choice when the parameters of the asset returns distribution, for example the mean vector and the covariance matrix, are unknown and have to be estimated by using historical data on asset returns. Our new approach employs the Baye ...
In this paper, new tests for the independence of two high-dimensional vectors are investigated. We consider the case where the dimension of the vectors increases with the sample size and propose multivariate analysis of variance-type statistics for the hypothesis of a block diago ...