منابع مشابه
Generalisations of Fisher Matrices
Fisher matrices play an important role in experimental design and in data analysis. Their primary role is to make predictions for the inference of model parameters—both their errors and covariances. In this short review, I outline a number of extensions to the simple Fisher matrix formalism, covering a number of recent developments in the field. These are: (a) situations where the data (in the ...
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Using Beck and Cohen’s superstatistics, we introduce in a systematic way a family of generalised Wishart-Laguerre ensembles of random matrices with Dyson index β = 1,2, and 4. The entries of the data matrix are Gaussian random variables whose variances η fluctuate from one sample to another according to a certain probability density f(η) and a single deformation parameter γ. Three superstatisti...
متن کاملOperator-valued Free Fisher Information of Random Matrices
We study the operator-valued free Fisher information of random matrices in an operator-valued noncommutative probability space. We obtain a formula for Φ M2(B) (A,A,M2(B), η), where A ∈ M2(B) is a 2 × 2 operator matrix on B, and η is linear operators on M2(B). Then we consider a special setting: A is an operator-valued semicircular matrix with conditional expectation covariance, and find that Φ...
متن کاملTOEPLITZ MATRICES WITH FISHER - HARTWIG SYMBOLS 3 norm of a
We describe the asymptotics of the spectral norm of finite Toeplitz matrices generated by functions with Fisher-Hartwig singularities as the matrix dimension goes to infinity. In the case of positive generating functions, our result provides the asymptotics of the largest eigenvalue, which is of interest in time series with long-range memory.
متن کاملNorms of Toeplitz Matrices with Fisher-Hartwig Symbols
we call a the symbol of the sequence {Tn} and denote Tn by Tn(a). The case where a is in L∞(T) is easy, since then ‖Tn(a)‖ → ‖a‖∞ as n → ∞. Things are more complicated for a ∈ L(T) \L∞(T). We here focus our attention on so-called FisherHartwig symbols with a single singularity, that is, we consider functions a of the form a(t) = |t− t0|φβ,t0(t)b(t) (t ∈ T) where t0 ∈ T, α is a complex number su...
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ژورنال
عنوان ژورنال: Entropy
سال: 2016
ISSN: 1099-4300
DOI: 10.3390/e18060236