We consider time series that, possibly after integer differencing or integrating or other detrending, are covariance stationary with spectral density that is regularly varying near zero frequency, and unspecified elsewhere. This semiparametric framework includes series with short, long and...

It is well-known that if a random vector X is in the generalized domain of attraction of the multivariate normal law (GDAN), then all its components are in the domain of attraction of the normal law (DAN) and, moreover, the Euclidean inner products of X with all the nonrandom vectors of unit...

Based on an R2-valued random sample {(yi,xi),1≤i≤n} on the simple linear regression model yi=xiβ+α+εi with unknown error variables εi, least squares processes (LSPs) are introduced in D[0,1] for the unknown slope β and intercept α, as well as for the unknown β when α=0. These LSPs...

For set-indexed partial sums processes of stationary mixing random fields, convergence of finite dimensional distributions to a Brownian motion is proved, extending to infinite variance previous results of the author and a Central Limit Theorem of Nahapetian. Gibbs fields are considered.