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Determining the dimension of the central subspace and central mean subspace
Biometrika, 2008The central subspace and central mean subspace are two important targets of sufficient dimension reduction. We propose a weighted chi-squared test to determine their dimensions based on matrices whose column spaces are exactly equal to the central subspace or the central mean subspace.
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Partial central subspace and sliced average variance estimation
Journal of Statistical Planning and Inference, 2009zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Shao, Yongwu +2 more
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Feature filter for estimating central mean subspace and its sparse solution
Computational Statistics & Data Analysis, 2021zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Wang, Pei +3 more
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Manuscripta Mathematica, 2011
A composition algebra is a (non-associative) algebra \((C, \ast )\) over a field \(F\), endowed with a non-degenerate quadratic ``norm form'' \(N: C \to F\), such that \(N(a \ast b) = N(a)N(b)\), \(a,b\in C\). Two special classes of these algebras have been fully classified.
Matzri, Eliyahu, Vishne, Uzi
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A composition algebra is a (non-associative) algebra \((C, \ast )\) over a field \(F\), endowed with a non-degenerate quadratic ``norm form'' \(N: C \to F\), such that \(N(a \ast b) = N(a)N(b)\), \(a,b\in C\). Two special classes of these algebras have been fully classified.
Matzri, Eliyahu, Vishne, Uzi
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Analysing nonlinear time series with central subspace
Journal of Statistical Computation and Simulation, 2012Traditionally, time series analysis involves building an appropriate model and using either parametric or nonparametric methods to make inference about the model parameters. Motivated by recent developments for dimension reduction in time series, an empirical application of sufficient dimension reduction (SDR) to nonlinear time series modelling is ...
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Fused Estimators of the Central Subspace in Sufficient Dimension Reduction
Journal of the American Statistical Association, 2014When studying the regression of a univariate variable Y on a vector x of predictors, most existing sufficient dimension-reduction (SDR) methods require the construction of slices of Y to estimate moments of the conditional distribution of X given Y. But there is no widely accepted method for choosing the number of slices, while a poorly chosen slicing ...
R. Dennis Cook, Xin Zhang
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Subspace Controllability of Quantum Ising Spin Networks with a Central Spin
2019 18th European Control Conference (ECC), 2019We consider a class of spin networks where each spin in a certain set interacts via Ising coupling with a single central spin. This is a common situation for instance in NV centers in diamonds. Due to the permutation symmetries of the network, the system is not globally controllable but it displays invariant subspaces of the underlying Hilbert space ...
Francesca Albertini +1 more
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Estimation and inference on central mean subspace for multivariate response data
Computational Statistics & Data Analysis, 2015zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zhu, Liping, Zhong, Wei
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Dimension reduction estimation for central mean subspace with missing multivariate response
Journal of Multivariate Analysis, 2019zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Fan, Guo-Liang +2 more
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