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ROBUST REGRESSION AND INTERPOLATION FOR TIME SERIES
Author(s) -
Taniguchi Masanobu
Publication year - 1981
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/j.1467-9892.1981.tb00311.x
Subject(s) - mathematics , residual , minimax , interpolation (computer graphics) , series (stratigraphy) , class (philosophy) , spectral density , statistics , mathematical optimization , algorithm , computer science , artificial intelligence , motion (physics) , paleontology , biology
. In this paper we shall consider the interpolation problem under the condition that the spectral density of a stationary process concerned is vaguely known (i.e., Huber's ε ‐contaminated model). Then we can get a minimax robust interpolator for the class of spectral densities S ={ g:g(x)=(1‐ε)f(x)+εh(x)ε Ar D o , 0<ε<1}, where f(x) is a known spectral density and D 0 is a certain class of spectral densities. Also we shall consider the time series regression problem under the condition that the residual spectral density is vaguely known. Then we can get a minimax robust regression coefficient estimate for the class of the residual spectral densities S .