Results 1  10
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741
On the distribution of the largest eigenvalue in principal components analysis
 ANN. STATIST
, 2001
"... Let x �1 � denote the square of the largest singular value of an n × p matrix X, all of whose entries are independent standard Gaussian variates. Equivalently, x �1 � is the largest principal component variance of the covariance matrix X ′ X, or the largest eigenvalue of a pvariate Wishart distribu ..."
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Cited by 422 (4 self)
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is defined in terms of the Painlevé II differential equation and can be numerically evaluated and tabulated in software. Simulations showthe approximation to be informative for n and p as small as 5. The limit is derived via a corresponding result for complex Wishart matrices using methods from random matrix
PAPER Special Section on Cryptography and Information Security A Construction of PublicKey Cryptosystem Based on Singular Simultaneous Equations
, 2005
"... SUMMARY Extensive studies have been made of the public key cryptosystems based on multivariate polynomials over F2. Howevermostofthe proposed public key cryptosystems based on multivariate polynomials, are proved not secure. In this paper, we propose several types of new constructions of public key ..."
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cryptosystems based on randomly generated singular simultaneous equations. One of the features of the proposed cryptosystems is that the sets of random singular simultaneous equations significantly enlarges the size of the transformation. key words: publickey cryptosystem, singular simultaneous equations
Marginalized kernels between labeled graphs
 Proceedings of the Twentieth International Conference on Machine Learning
, 2003
"... A new kernel function between two labeled graphs is presented. Feature vectors are defined as the counts of label paths produced by random walks on graphs. The kernel computation finally boils down to obtaining the stationary state of a discretetime linear system, thus is efficiently performed by s ..."
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Cited by 194 (15 self)
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by solving simultaneous linear equations. Our kernel is based on an infinite dimensional feature space, so it is fundamentally different from other string or tree kernels based on dynamic programming. We will present promising empirical results in classification of chemical compounds. 1 1.
Singular Perturbations In Option Pricing
 SIAM J. Applied Math
, 2002
"... After the celebrated BlackScholes formula for pricing call options under constant volatility, the need for more general nonconstant volatility models in financial mathematics has been the motivation of numerous works during the Eighties and Nineties. In particular, a lot of attention has been paid ..."
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Cited by 41 (11 self)
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in capturing the effects of random volatility in simple robust corrections to constant volatility formulas. From the point of view of partial differential equations this method corresponds to a singular perturbation analysis. The aim of this paper is to deal with the nonsmoothness of the payoff function
Fredholm Determinants, Differential Equations and Matrix Models
 COMMUNICATIONS IN MATHEMATICAL PHYSICS
, 1994
"... Orthogonal polynomial random matrix models of N x N hermitian matrices lead to Fredholm determinants of integral operators with kernel of the form (φ(x)φ(y) — ψ(x)φ(y))/x — y. This paper is concerned with the Fredholm determinants of integral operators having kernel of this form and where the und ..."
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Cited by 142 (20 self)
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Orthogonal polynomial random matrix models of N x N hermitian matrices lead to Fredholm determinants of integral operators with kernel of the form (φ(x)φ(y) — ψ(x)φ(y))/x — y. This paper is concerned with the Fredholm determinants of integral operators having kernel of this form and where
Random Coefficients on Endogenous Variables in Simultaneous Equations Models ∗
, 2012
"... This paper considers a classical linear simultaneous equations model with random coefficients on the endogenous variables. Simultaneous equations models are used to study social interactions, strategic interactions between firms, and market equilibrium. Random coefficient models allow for heterogene ..."
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Cited by 3 (0 self)
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This paper considers a classical linear simultaneous equations model with random coefficients on the endogenous variables. Simultaneous equations models are used to study social interactions, strategic interactions between firms, and market equilibrium. Random coefficient models allow
Bayesian Simultaneous Equations Analysis using Reduced Structures
, 1997
"... Diffuse priors lead to pathological posterior behavior when used in Bayesian analyses of Simultaneous Equation Models (SEMs). This results from the local nonidentication of certain parameters in SEMs. When this, a priori known, feature is not captured appropriately, an a posteriori favor for certain ..."
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Cited by 39 (3 self)
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Diffuse priors lead to pathological posterior behavior when used in Bayesian analyses of Simultaneous Equation Models (SEMs). This results from the local nonidentication of certain parameters in SEMs. When this, a priori known, feature is not captured appropriately, an a posteriori favor
Application of the τfunction theory of Painlevé equations to random matrices
 PV, PIII, the LUE, JUE and CUE
, 2002
"... Okamoto has obtained a sequence of τfunctions for the PVI system expressed as a double Wronskian determinant based on a solution of the Gauss hypergeometric equation. Starting with integral solutions of the Gauss hypergeometric equation, we show that the determinant can be reexpressed as multidim ..."
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Cited by 75 (20 self)
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characterisation in terms of a difference equation. In the case of the cJUE, the spectrum singularity scaled limit is considered, and the evaluation of a certain four parameter average is given in terms of the general PV transcendent in σ form. Applications are given to the evaluation of the spacing distribution
SIMULTANEOUS SYSTEM OF SPATIAL AUTOREGRESSIVE EQUATIONS WITH RANDOM EFFECTS
"... 2012 $5.00 Uptodate information about CPR’s research projects and other activities is available from our World Wide Web site at www.maxwell.syr.edu/cpr.aspx. All recent working papers and Policy Briefs can be read and/or printed from there as ..."
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2012 $5.00 Uptodate information about CPR’s research projects and other activities is available from our World Wide Web site at www.maxwell.syr.edu/cpr.aspx. All recent working papers and Policy Briefs can be read and/or printed from there as
BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS WITH RANDOM STOPPING TIME AND SINGULAR FINAL CONDITION
, 2007
"... In this paper we are concerned with onedimensional backward stochastic differential equations (BSDE in short) of the following type: Yt = ξ − ..."
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Cited by 6 (2 self)
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In this paper we are concerned with onedimensional backward stochastic differential equations (BSDE in short) of the following type: Yt = ξ −
Results 1  10
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741