Radial-like Toeplitz operators on Cartan domains of type I are a set of linear partial differential equations that have been used to describe a variety of physical phenomena such as the scattering of acoustic and elastic waves, the propagation of electromagnetic radiation, and the propagation of sound waves in inhomogeneous media. They are usually studied in the real or complex domain, depending on the application at hand.
Data can be assumed to be continuous functions defined on an infinite-dimensional space for many phenomena. However, the infinite-dimensional data might be driven by a small number of latent variables. Hence, factor models are relevant for functional data. In this paper, we study functional factor models for time-dependent functional data. We propose nonparametric estimators under stationary and nonstationary processes. We obtain estimators that consider the time-dependence property. Specifically, we use the information contained in the covariances at different lags. We show that the proposed estimators are consistent. Through Monte Carlo simulations, we find that our methodology outperforms estimators based on functional principal components. We also apply our methodology to monthly yield curves. In general, the suitable integration of time-dependent information improves the estimation of the latent factors.
The non-central Wishart and inverted Wishart distributions are studied in this work
under elliptical models; some distributional results are based on some generalizations of the wellknown Kummer relations, which leds us to determine that some moments have a polynomial
representation. Then the non-central F and “studentized Wishart” distributions are derived in a
general setting. After some generalizations, including the so called non-central generalized inverted
Wishart distribution, the classical results based on Gaussian models are derived here as corollaries.
