First and second order analysis for periodic random arrays using block bootstrap methods

First and second order analysis for periodic random arrays using block bootstrap methods

In the paper row-wise periodically correlated triangular arrays are considered. The period length is assumed to grow in time. The Fourier decomposition of the mean and autocovariance functions for each row of the matrix is presented. To construct bootstrap estimators of the Fourier coefficients two block bootstrap techniques are used. These are the circular version of the Generalized Seasonal B...

Bootstrap for the second-order analysis of Poisson-sampled almost periodic processes

In this paper we consider a continuous almost periodically correlated process {X(t), t ∈ R} that is observed at the jump moments of a stationary Poisson point process {N(t), t ≥ 0}. The processes {X(t), t ∈ R} and {N(t), t ≥ 0} are assumed to be independent. We define the kernel estimators of the Fourier coefficients of the autocovariance function of X(t) and investigate their asymptotic proper...

First- and Second-order Adaptive Differential Microphone Arrays

Whenever undesired noise sources are spatially nonstationary, conventional directional microphone technology has its limits in terms of interference suppression. Adaptive differential microphone arrays (ADMAs) with their null steering capabilities promise better performance. This contribution introduces and examines firstand second-order ADMAs based on fullband as well as on subband algorithms....

Almost Periodic Solutions of First- and Second-Order Cauchy Problems

Almost periodicity of solutions of firstand second-order Cauchy problems on the real line is proved under the assumption that the imaginary (resp. real) spectrum of the underlying operator is countable. Related results have been obtained by Ruess Vu~ and Basit. Our proof uses a new idea. It is based on a factorisation method which also gives a short proof (of the vector-valued version) of Loomi...

Autoregressive Gaussian Random Vectors of First Order