Smoothing spline ANOPOW

This paper is motivated by the pioneering work of Emanuel Parzen wherein he advanced the estimation of (spectral) densities via kernel smoothing and established the role of reproducing kernel Hilbert spaces (RKHS) in field of time series analysis. Here, we consider analysis of power (ANOPOW) for replicated time series collected in an experimental design where the main goals are to estimate, and to detect differences among, group spectra. To accomplish these goals, we obtain smooth estimators of the group spectra by assuming that each spectral density is in some RKHS; we then apply penalized least squares in a smoothing spline ANOPOW. For inference, we obtain simultaneous confidence intervals for the estimated group spectra via bootstrapping.