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RATE OF CONVERGENCE FOR LOGSPLINE SPECTRAL DENSITY ESTIMATION
Author(s) -
Kooperberg Charles,
Stone Charles J.,
Truong Young K.
Publication year - 1995
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.1467-9892.1995.tb00241.x
Subject(s) - mathematics , rate of convergence , logarithm , infinity , polynomial , spectral density , convergence (economics) , periodogram , nonparametric statistics , density estimation , function (biology) , mathematical analysis , statistics , estimator , channel (broadcasting) , economic growth , electrical engineering , economics , engineering , evolutionary biology , biology
. The logarithm of the spectral density function for a stationary process is approximated by polynomial splines. The approximation is chosen to maximize the expected log‐likelihood based on the asymptotic properties of the periodogram. Estimates of this approximation are shown to possess the usual nonparametric rate of convergence when the number of knots suitably increases to infinity.