The purpose of this paper is to investigate kernel density estimators for spatial processes with linear or nonlinear structures. Sufficient conditions for such estimators to converge in L1 are obtained under extremely general, verifiable conditions. The results hold for mixing as well as for...

Since the pioneering work of Koenker and Bassett, median-restricted models have attracted considerable interest. Attention in these models, so far, has focused on least absolute deviation (auto-)regression quantile estimation and the corresponding sign tests. These methods use a pseudolikelihood...

Conditions for mixed autoregressive-moving average processes with time-dependent coefficients to be purely nondeterministic and invertible can be obtained from classical difference equations theory. These conditions involve one-sided Green's functions or their matricial equivalents. A recursive...

The assumption of homogeneity of covariance matrices is the fundamental prerequisite of a number of classical procedures in multivariate analysis. Despite its importance and long history, however, this problem so far has not been completely settled beyond the traditional and highly unrealistic...

Traditional AR order-identification methods rely on an inspection of partial correlograms. The rank-based version of partial correlograms is investigated here. Unlike the rank-based versions of Lagrange multiplier test statistics considered in Hallin and Puri (1994, J. Multivariate Anal. 50,...

A nonstationary generalization of the classical Yule-Walker equations, relating the (time-varying) autocorrelations of an autoregressive process to the coefficients of the possible models for this process, is given. The corresponding theoretical model-building (or spectral factorization)...