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March, 1974 Estimating the Kernels of Nonlinear Orthogonal Polynomial Functionals
Benjamin Kimelfeld
Ann. Statist. 2(2): 353-358 (March, 1974). DOI: 10.1214/aos/1176342669

Abstract

Let $(X(t), Y(t))$ be a complex vector process stationary of order $k$ for any $k, k = 1,2,\cdots$, such that $Y(t)$ is expressed as a polynomial functional of degree 2 operating on $X(t)$. Then $Y(t)$ can be rewritten as a sum of orthogonal projections $G_j(K_j, Y(t)), j = 0, 1, 2$. It is shown that there is a set of functionals which approximate in mean square the projection $G_2(K_2, Y(t))$. Moreover, it is possible to determine the kernels associated with these functionals.

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Benjamin Kimelfeld. "Estimating the Kernels of Nonlinear Orthogonal Polynomial Functionals." Ann. Statist. 2 (2) 353 - 358, March, 1974. https://doi.org/10.1214/aos/1176342669

Information

Published: March, 1974
First available in Project Euclid: 12 April 2007

zbMATH: 0277.60021
MathSciNet: MR394831
Digital Object Identifier: 10.1214/aos/1176342669

Subjects:
Primary: 60G10
Secondary: 62M10

Keywords: cumulant spectrum , ‎kernel‎ , lag process , orthogonal polynomial functional , ‎spectral representation , stationary stochastic process

Rights: Copyright © 1974 Institute of Mathematical Statistics

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