STATISTICAL INFERENCE ON TIME SERIES BY RKHS METHODS.

By Emanuel Parzen. 1970

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Citations in the corpus

Kernel methods in machine learning (2007, neutral): “In addition to the above uses of positive definite kernels in machine learning, there has been a parallel, and partly earlier development in the field of statistics, where such kernels have been used, for instance, for time series analysis (Parzen [106]), as well as regression estimation and the sol”
Linear Inverse Problems in Structural Econometrics Estimation Based on Spectral Decomposition and Regularization (2003, methodology): “Such a mapping J is called a Hilbert space isomorphism (or congruence) from H1 to H2: The terminology congruence is used by Parzen (1959, 1970).”
Canonical correlation for stochastic processes (2008, background): “In particular, we will state, without proof, some basic facts about RKHSs. Verification of these results as well as more detailed discussions of RKHS theory can be found in Aronszajn [2], Parzen [24], Weinert [35] and Berlinet and Thomas-Agnan [6].”
Efficient estimation of general dynamic models with a continuum of moment conditions (2007, background): “As discussed in Carrasco and Florens (2000), the operator K−1/2 does not exist on the whole space L2 (π) but only on a subset, denoted H (K) , which corresponds to the socalled reproducing kernel Hilbert space (RKHS) associated with K (see Parzen, 1970, and Carrasco and Florens, 2004, for details).”
GENERALIZATION OF GMM TO A CONTINUUM OF MOMENT CONDITIONS (2000, methodology): “De�nition 8 ( Parzen, 1970 ) Every symmetric nonnegative de�nite kernel k de�ning”
ON THE ASYMPTOTIC EFFICIENCY OF GMM (2013, background): “Using results by Parzen (1959, 1970), we show that the asymptotic variance can be rewritten as an inner product in a dual space of the RKHS that is easier to handle.”