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Träfflista för sökning "hsv:(NATURVETENSKAP) hsv:(Matematik) hsv:(Sannolikhetsteori och statistik) ;pers:(Podgórski Krzysztof)"

Sökning: hsv:(NATURVETENSKAP) hsv:(Matematik) hsv:(Sannolikhetsteori och statistik) > Podgórski Krzysztof

  • Resultat 1-10 av 90
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1.
  • Bodnar, Taras, et al. (författare)
  • A test for the global minimum variance portfolio for small sample and singular covariance
  • 2017
  • Ingår i: AStA Advances in Statistical Analysis. - : Springer. - 1863-8171 .- 1863-818X. ; 101:3, s. 253-265
  • Tidskriftsartikel (refereegranskat)abstract
    • Recently, a test dealing with the linear hypothesis for the global minimum variance portfolio weights was obtained under the assumption of non-singular covariance matrix. However, the problem of potential multicollinearity and correlations of assets constitutes a limitation of the classical portfolio theory. Therefore, there is an interest in developing theory in the presence of singularities in the covariance matrix. In this paper, we extend the test by analyzing the portfolio weights in the small sample case with a singular population covariance matrix. The results are illustrated using actual stock returns and a discussion of practical relevance of the model is presented. 
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2.
  • Bodnar, Taras, et al. (författare)
  • Singular inverse Wishart distribution and its application to portfolio theory
  • 2016
  • Ingår i: Journal of Multivariate Analysis. - : Elsevier BV. - 0047-259X .- 1095-7243. ; 143, s. 314-326
  • Tidskriftsartikel (refereegranskat)abstract
    • The inverse of the standard estimate of covariance matrix is frequently used in the portfolio theory to estimate the optimal portfolio weights. For this problem, the distribution of the linear transformation of the inverse is needed. We obtain this distribution in the case when the sample size is smaller than the dimension, the underlying covariance matrix is singular, and the vectors of returns are independent and normally distributed. For the result, the distribution of the inverse of covariance estimate is needed and it is derived and referred to as the singular inverse Wishart distribution. We use these results to provide an explicit stochastic representation of an estimate of the mean-variance portfolio weights as well as to derive its characteristic function and the moments of higher order. The results are illustrated using actual stock returns and a discussion of practical relevance of the model is presented.
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3.
  • Bodnar, Taras, et al. (författare)
  • Tangency portfolio weights for singular covariance matrix in small and large dimensions : estimation and test theory
  • 2019
  • Ingår i: Journal of Statistical Planning and Inference. - : Elsevier. - 0378-3758 .- 1873-1171. ; 201, s. 40-57
  • Tidskriftsartikel (refereegranskat)abstract
    • In this paper we derive the finite-sample distribution of the estimated weights of the tangency portfolio when both the population and the sample covariance matrices are singular. These results are used in the derivation of a statistical test on the weights of the tangency portfolio where the distribution of the test statistic is obtained under both the null and the alternative hypotheses. Moreover, we establish the high-dimensional asymptotic distribution of the estimated weights of the tangency portfolio when both the portfolio dimension and the sample size increase to infinity. The theoretical findings are implemented in an empirical application dealing with the returns on the stocks included into the S&P 500 index. 
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4.
  • Bogsjö, Klas, et al. (författare)
  • Models for road surface roughness
  • 2012
  • Ingår i: Vehicle System Dynamics. - : Informa UK Limited. - 0042-3114 .- 1744-5159. ; 50:5, s. 725-747
  • Tidskriftsartikel (refereegranskat)abstract
    • This study focuses on the statistical description and analysis of road surface irregularities that are essential for heavy-vehicle fatigue assessment. Three new road profile models are proposed: a homogenous Laplace moving average process, a non-homogenous Laplace process and a hybrid model that combines Gaussian and Laplace modelling. These are compared with the classical homogenous Gaussian process as well as with the non-homogenous Gaussian model that represents the road surface as a homogenous Gaussian process with Motor Industry Research Association spectrum enhanced by randomly placed and shaped irregularities. The five models are fitted to eight measured road surfaces and their accuracy and efficiency are discussed.
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5.
  • Johannesson, Pär, 1969, et al. (författare)
  • Laplace distribution models for road topography and roughness
  • 2017
  • Ingår i: International Journal of Vehicle Performance. - 1745-3194 .- 1745-3208. ; 3:3, s. 224-258
  • Tidskriftsartikel (refereegranskat)abstract
    • Gaussian models are frequently used for road elevations. However,these models are often only valid for short sections of the road. Here we presenta comprehensive approach to describe various aspects of road surface/elevationby using extensions of Gaussian models arising from random gamma distributedvariances. These random variances result in the Laplace distribution and thuswe refer to the so defined models as Laplace models. The approach is shownto perform well in modelling road topography, road roughness and multi-valuedresponses of forces and bending moments containing transients. The differentLaplace models are presented together with numerical examples and Matlab codefor simulation.
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6.
  • Podgorski, Krzysztof, et al. (författare)
  • Distributions at random events
  • 2016
  • Ingår i: 2016 2ND INTERNATIONAL CONFERENCE ON EVENT-BASED CONTROL, COMMUNICATION, AND SIGNAL PROCESSING (EBCCSP). - 9781509041961 ; , s. 1-8
  • Konferensbidrag (refereegranskat)abstract
    • We discuss the generalized Rice formula approach to deriving long-run distributions of characteristics defined at random events of a stochastic process or field. The approach stems from the same principle originally introduced by Rice for the level crossing intensity in a random signal and we review its extensions to more general contexts.Events are defined on random surfaces through crossing levels of (multivariate) stochastic fields.We also account for the dynamics of spatial-temporal fields using observed velocities. Extensions beyond the Gaussian model are shown and models for sampling from the level crossing distributions are presented.The importance of these generalizations for applications is illustrated through examples.
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7.
  • Podgorski, Krzysztof, et al. (författare)
  • Distributions of spatial wave size for random fields
  • 2016
  • Ingår i: 2nd International Conference on Event-Based Control, Communication, and Signal Processing (EBCCSP), Krakow, POLAND, JUN 13-15, 2016. - 9781509041961
  • Konferensbidrag (refereegranskat)abstract
    • A method of measuring three-dimensional spatial wave size is proposed and statistical distributions of the size characteristics are derived in explicit integral forms for Gaussian sea surfaces. New definitions of wave characteristics such as the crest-height, the length, the size and the wave front location are provided in fully dimensional context. The joint statistical distributions of these wave characteristics are derived using the Rices formulas for expected numbers of local maximum and distance from a local maximum to a level crossing countour. %The methodology will be also illustrated by some examples from other type of engineering applications. Review of the Rice's method to study crossing distributions is given.
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8.
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9.
  • Johannesson, Pär, 1969, et al. (författare)
  • Modelling roughness of road profiles on parallel tracks using roughness indicators
  • 2014
  • Annan publikation (övrigt vetenskapligt/konstnärligt)abstract
    • The vertical road input is the most important load for durability assessments of vehicles. We focus on stochastic modelling of the parallel road profiles with the aim to find a simple but still accurate model for such bivariate records. A model is proposed that is locally Gaussian with randomly gamma distributed variances leading to a generalized Laplace distribution of the road profile. This Laplace model is paired with the ISO spectrum and is specified by only three parameters. Two of them can be estimated directly from a sequence of roughness indicators, such as IRI or ISO roughness coefficient. The third parameter needed to define the cross spectrum between the left and right road profiles is estimated from the sample correlation. Explicit approximations for the expected fatigue damage for the proposed Laplace-ISO model are developed and its usefulness is validated using measured road profiles.
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10.
  • Lindgren, Georg, et al. (författare)
  • Effective persistency evaluation via exact excursion distributions for random processes and fields
  • 2022
  • Ingår i: Journal of Physics Communications. - : IOP Publishing. - 2399-6528. ; 6
  • Tidskriftsartikel (refereegranskat)abstract
    • Finding the probability that a stochastic system stays in a certain region of its state space over a specified time—a long-standing problem both in computational physics and in applied and theoretical mathematics—is approached through the extended and multivariate Rice formula. In principle, it applies to any smooth process multivariate both in argument and in value given that efficient numerical implementations of the high-dimensional integration are available. The computational method offers an exact integral representation yielding remarkably accurate results and provides an alternative method of computing persistency probability and exponent for a physical system. It can be viewed as an implementation of path integration for a smooth Gaussian process with an arbitrary covariance. Its high accuracy is due to efficient computation of expectations with respect to high-dimensional nearly singular Gaussian distributions. For Gaussian processes, the computations are effective and more precise than those based on the Rice series expansions and the independent interval approximation. For the benchmark diffusion process, it produces the persistency exponent that is essentially the same as the recently obtained analytical value and surpasses accuracy, interpretability as well as control of the error, previous methods including the independent or Markovian approximation. The method solves the two-step excursion dependence for a stationary differentiable Gaussian process, in both theoretical and numerical sense. The solution is based on exact expressions for the probability density for one and two successive excursion lengths. The numerical routine RIND computes the densities using recent advances in scientific computing and is easily accessible for a general covariance function, via a simple numerical interface. The work offers also analytical results that explain the effectiveness of the implemented methodology and elaborates its utilization for non-Gaussian processes.
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