QRegEstimator-class: Class for quantile regression-based estimates in the harmonic linear model.
Description
QRegEstimator is an S4 class that implements the
necessary calculations to determine the frequency
representation based on the weigthed
$L_1$-projection of a time series as described in
Dette et. al (2014+). As a subclass to
FreqRep it inherits slots and methods defined
there.Details
For each frequency $\omega$ from frequencies
and level $\tau$ from levels the statistic
$$\hat b^{\tau}_n(\omega) := \arg\max_{a \in R, b \in
C} \sum_{t=0}^{n-1} \rho_{\tau}(Y_t - a - Re(b) \cos(\omega
t) - Im(b) \sin(\omega t)),$$ is determined and stored to
the array values.
The solution to the minimization problem is determined
using the function rq from the
quantreg package.
All remarks made in the documentation of the super-class
FreqRep apply.References
Dette, H., Hallin, M., Kley, T. & Volgushev, S. (2014+). Of
Copulas, Quantiles, Ranks and Spectra: an
$L_1$-approach to spectral analysis.
Bernoulli, forthcoming.