We propose two techniques for the fast numerical implementation of a random vector transform within Wiener filtering paradigm. In signal processing terminology, the transform is interpreted as an ...optimal filter. The proposed transform aims to minimize the sum of distances between a reference random vector xi and its transformed counterpart yi, for all i=1,…,p. In contrast to known techniques where the transform consists of p matrices that minimize a difference between a single reference random vector and p observed random vectors, the proposed transform uses a single optimal matrix to transform p random vectors. It requires less computational work for the numerical implementation. Nevertheless, a direct numerical realization of the transform involves computation of the covariance matrix pseudo-inverse and the matrix square root which might be large, and then are computationally expensive. Proposed fast versions of the transform allow us to avoid that computation and, as a result, accelerate the numerical implementation. While the fast proposed techniques are approximate versions of the original transform, it is shown that their accuracies are very close to those of the original transform. An error analysis is provided. The effectiveness of the proposed transform is illustrated by numerical experiments in four real-world scenarios.
In this paper, the weak laws of large numbers for weighted sums and random sums of H-valued dependent random vectors are established, which include and generalize some known results. As an ...application, the concept of CWOD random vectors is introduced and the corresponding weak laws of large numbers for weighted sums and random sums cases are obtained. Furthermore, to complete the work of Anh and Hien (2021), the weak law of large numbers for random sums of PCND random vectors is also presented.
The paper addresses a problem of sampling discretization of integral norms of elements of finite-dimensional subspaces satisfying some conditions. We prove sampling discretization results under a ...standard assumption formulated in terms of the Nikol'skii-type inequality. In particular, we obtain some upper bounds on the number of sample points sufficient for good discretization of the integral Lp norms, 1≤p<2, of functions from finite-dimensional subspaces of continuous functions. Our new results improve upon the known results in this direction. We use a new technique based on deep results of Talagrand from functional analysis.
This paper develops almost sure convergence for sums of negatively superadditive dependent random vectors in Hilbert spaces, we obtain Chung type SLLN and the Jaite type SLLN for sequences of ...negatively superadditive dependent random vectors in Hilbert spaces. Rate of convergence is studied through considering almost sure convergence to 0 of tail series. As an application, the almost sure convergence of degenerate von Mises-statistics is investigated.
The stability of Bernstein's characterization of Gaussian distributions is extended to vectors by utilizing characteristic functions. Stability is used to develop a soft doubling argument that ...establishes the optimality of Gaussian vectors for certain communications channels with additive Gaussian noise, including two-receiver broadcast channels. One novelty is that the argument does not require the existence of distributions that achieve capacity.
Kinetic energies in random vectors Daia, Alexandru; Stancu, Stelian; Suchak, Om
Proceedings of the International Conference on Applied Statistics,
12/2020, Letnik:
2, Številka:
1
Journal Article
Recenzirano
Odprti dostop
This paper uses the Onicescu Coefficient concept, which is the sum of squared probabilities, through mathematical formulations to show the kinetic energy in random vectors. The paper has a brief ...introduction section that addresses the background of the study, the purpose of the study, and its objective. The literature review section provides an in-depth industrial application of mathematical formulations in solving real-life problems. The paper contains a methodology section highlighting the study design, data collection methods, and analysis section, highlighting some of the keywords used in locating resources and significant databases that provided the study with information. Later, the study takes the result and discussion sectional approach to present the experiments’ findings backed with facts from previous studies by other scholars in the same field. Lastly, the paper concludes with a section recapping the critical points of this study and study application in real-life, concluding with a list of references utilized by this study.
Kinetic energies in random vectors Daia, Alexandru; Stancu, Stelian; Suchak, Om
Proceedings of the International Conference on Applied Statistics,
12/2020, Letnik:
2, Številka:
1
Journal Article
Recenzirano
Odprti dostop
This paper uses the Onicescu Coefficient concept, which is the sum of squared probabilities, through mathematical formulations to show the kinetic energy in random vectors. The paper has a brief ...introduction section that addresses the background of the study, the purpose of the study, and its objective. The literature review section provides an in-depth industrial application of mathematical formulations in solving real-life problems. The paper contains a methodology section highlighting the study design, data collection methods, and analysis section, highlighting some of the keywords used in locating resources and significant databases that provided the study with information. Later, the study takes the result and discussion sectional approach to present the experiments’ findings backed with facts from previous studies by other scholars in the same field. Lastly, the paper concludes with a section recapping the critical points of this study and study application in real-life, concluding with a list of references utilized by this study.
PDF
