A Test for a Difference Between Spectral Peak Frequencies

Introduction Spectral analysis is frequently applied to investigate oscillatory phenomena in basic medical and biological research (Marsden et al., 1969a; Marsden et al., 1969b; Nelson et al., 1979; Gunther, Brunner and Klußmann, 1983; Cleeves and Findley, 1987; Hefter et al., 1987; Clayton et al. 1995; Beuter, 1996; Pinna, Maestri, Di Cesare, 1996; Hutchinson et al., 1997) and medical treatment monitoring (Herrmann, 1982; Khutorskaya and Fjodorova, 1996). Usually, the peak frequency and the power of the oscillation are of major interest. Often, it is desirable to decide whether differences in the observed spectral peak frequencies of two estimated spectra are significant, i.e. to test the hypothesis of a zero peak frequency difference. We propose a procedure to test this hypothesis. It is inspired by the parametric bootstrap (Efron and Tibshirani, 1993) and the theory of the spectral estimation (Brockwell and Davis, 1987). General aspects of bootstrapping in the frequency do