Nonlinear functional models for functional responses in reproducing kernel hilbert spaces

By Heng Lian. 2007

78 citations recorded by the source corpus.

The author proposes an extension of reproducing kernel Hilbert space theory which provides a new framework for analyzing functional responses with regression models. The approach only presumes a general nonlinear regression structure, as opposed to existing linear regression models. The author proposes generalized cross‐validation for automatic smoothing parameter estimation. He illustrates the use of the new estimator both on real and simulated data.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/002a8710cbfe1fe07e02b750904c0bcf14c6cec4

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

In Computational Theory and Mathematics

In Geometry and Topology

Citations in the corpus

Empirical likelihood confidence intervals for nonparametric functional data analysis (2009, methodology): “More recently, there has also been some studies using alternative nonparametric techniques such as reproducing kernel Hilbert spaces (Preda, 2007; Hernandez et al., 2007), and dealing with the case where the dependent variables are curves as well (Cuevas et al., 2002; Lian, 2007).”
Nonlinear functional regression: a functional RKHS approach (2010, background): “We show that classical results on RKHS may be straitforwardly extended to functional RKHS (Lian, 2007; Preda, 2007); the representer theorem is restated in this context; the construction of operator kernels is also discussed, and we exhibit a counterpart of the Gaussian kernel for this setting.”
Support Distribution Machines (2012, methodology): “Inspired by this, Lian (2007) and Kadri et al. (2010) generalized the functional regression problem to functional responses as well.”
Operator-valued Kernels for Learning from Functional Response Data (2015, methodology): “nts (predictors or responses) that may be viewed as random curves. In this context, though some concepts on the use of RKHS for functional data similar to those presented in this work can be found in Lian (2007), the present paper provides a much more complete view of learning from functional data u”
Shrinkage estimation and selection for multiple functional regression (2011, methodology): “Besides these two major approaches, other methods such as putting functional regression in the reproducing kernel Hilbert space framework has been developed (Preda, 2007; Lian, 2007).”
Multiple Operator-valued Kernel Learning (2012, background): “In addition, some works on functional regression and structured-output learning consider operator-valued kernels constructed from the identity operator as in [19] and [4].”
A Generalized Kernel Approach to Structured Output Learning (2012, unknown): “been focused on extending these kernels to the domain of functional data analysis to deal with the problem of regression with functional responses, where outputs are considered to be in the L2-space (Lian, 2007; Kadri et al., 2010). However, the operator- valued Kernels used in these contexts for di”
Convergence of functional k-nearest neighbor regression estimate with functional responses (2011, methodology): “Another nonparametric approach is based on the reproducing kernel Hilbert spaces framework [18, 15].”