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Longitudinal data analysis using generalized linear models”.
 Biometrika,
, 1986
"... SUMMARY This paper proposes an extension of generalized linear models to the analysis of longitudinal data. We introduce a class of estimating equations that give consistent estimates of the regression parameters and of their variance under mild assumptions about the time dependence. The estimating ..."
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Cited by 1526 (8 self)
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. The estimating equations are derived without specifying the joint distribution of a subject's observations yet they reduce to the score equations for multivariate Gaussian outcomes. Asymptotic theory is presented for the general class of estimators. Specific cases in which we assume independence, m
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
Multivariate Stochastic Approximation Using a Simultaneous Perturbation Gradient Approximation
 IEEE TRANSACTIONS ON AUTOMATIC CONTROL
, 1992
"... Consider the problem of finding a root of the multivariate gradient equation that arises in function minimization. When only noisy measurements of the function are available, a stochastic approximation (SA) algorithm of the general KieferWolfowitz type is appropriate for estimating the root. This p ..."
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Cited by 318 (14 self)
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Consider the problem of finding a root of the multivariate gradient equation that arises in function minimization. When only noisy measurements of the function are available, a stochastic approximation (SA) algorithm of the general KieferWolfowitz type is appropriate for estimating the root
Algebraic Attacks on Stream Ciphers with Linear Feedback
, 2003
"... A classical construction of stream ciphers is to combine several LFSRs and a highly nonlinear Boolean function f . Their security is usually studied in terms of correlation attacks, that can be seen as solving a system of multivariate linear equations, true with some probability. At ICISC'0 ..."
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Cited by 262 (21 self)
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A classical construction of stream ciphers is to combine several LFSRs and a highly nonlinear Boolean function f . Their security is usually studied in terms of correlation attacks, that can be seen as solving a system of multivariate linear equations, true with some probability. At ICISC
An efficient FHE proposal based on the hardness of solving systems of nonlinear multivariate equations (II)
"... Abstract. We propose a general framework to develop fully homomorphic encryption schemes (FHE) without using Gentry’s technique. Initially, a privatekey cryptosystem is built over Zn (n being an RSA modulus). An encryption of x ∈ Zn is a randomly chosen vector e such that Φ(e) = x where Φ is a sec ..."
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secret multivariate polynomial. This privatekey cryptosystem is not homomorphic in the sense that the vector sum is not a homomorphic operator. Nonlinear homomorphic operators are then developed. The security relies on the difficulty of solving systems of nonlinear equations (which is a NP
Efficient Algorithms for Solving Overdefined Systems of Multivariate Polynomial Equations
 IN ADVANCES IN CRYPTOLOGY, EUROCRYPT’2000, LNCS 1807
, 2000
"... The security of many recently proposed cryptosystems is based on the difficulty of solving large systems of quadratic multivariate polynomial equations. This problem is NPhard over any field. When the number of equations m is the same as the number of unknowns n the best known algorithms are exhaus ..."
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Cited by 182 (20 self)
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The security of many recently proposed cryptosystems is based on the difficulty of solving large systems of quadratic multivariate polynomial equations. This problem is NPhard over any field. When the number of equations m is the same as the number of unknowns n the best known algorithms
MICE: Multivariate Imputation by Chained Equations in R
"... Multivariate Imputation by Chained Equations (MICE) is the name of software for imputing incomplete multivariate data by Fully Conditional Specification (FCS). MICE V1.0 appeared in the year 2000 as an SPLUS library, and in 2001 as an R package. MICE V1.0 introduced predictor selection, passive imp ..."
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Cited by 145 (1 self)
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Multivariate Imputation by Chained Equations (MICE) is the name of software for imputing incomplete multivariate data by Fully Conditional Specification (FCS). MICE V1.0 appeared in the year 2000 as an SPLUS library, and in 2001 as an R package. MICE V1.0 introduced predictor selection, passive
Multivariate Simultaneous Generalized Arch
, 1993
"... This paper presents theoretical results in the formulation and estimation of multivariate generalized ARCH models within simultaneous equations systems. A new parameterization of the multivariate ARCH process is proposed and equivalence relations are discussed for the various ARCH parameterizations. ..."
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Cited by 145 (2 self)
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This paper presents theoretical results in the formulation and estimation of multivariate generalized ARCH models within simultaneous equations systems. A new parameterization of the multivariate ARCH process is proposed and equivalence relations are discussed for the various ARCH parameterizations
multivariable
, 2012
"... Remaining life prognostics of rolling bearing based on relative features and ..."
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Remaining life prognostics of rolling bearing based on relative features and
Results 1  10
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70,090