Inference on periodograms of infinite dimensional discrete time periodically correlated processes

In this work we shall consider two classes of weakly second-order periodically correlated and strongly second-order periodically correlated processes with values in separable Hilbert spaces. The periodogram for these processes is introduced and its statistical properties are studied. In particular, it is proved that the periodogram is asymptotically unbiased for the spectral density of the processes, where the type of the convergence is fully specified.     

Weakly Periodic Sequences of Bounded Linear Transformations: a Spectral Characterization

Let X and Y be two Hilbert spaces, and the space of bounded linear transformations from X into Y. Let {A } be a weakly periodic sequence of period T. Spectral theory of weakly periodic sequences in a Hilbert space is studied by H. L. Hurd and V. Mandrekar (1991). In this work we proceed further to characterize {A _n} by a positive measure and a number T of -valued functions a ₀, . . . ,a _T–1; in the spectral form , where and is an -valued Borel set function on [0, 2) such that      

A Spectral Representation for Weakly Periodic Sequences F Bounded Linear Transformations

A spectral representation for certain sequences of bounded linear transformations between two Hilbert spaces, namely; weakly periodic, is given. In this representation the elements of a weakly periodic sequence, {An, n Z} L(X, Y), are viewed, in the weak sense, as the Fourier coefficients of a certain set function on the Borel sets of [0, 2) with values in L(X, Y).     

Separation,preconcentration and speciation of chromium by solid phase extraction on immobilised ferron

A sensitive and simple method for determination of chromium species after separation and preconcentration by solid phase extraction (SPE) has been developed. For the determination of the total concentration of chromium in solution, Cr(VI) was efficiently reduced to Cr(III) by addition of hydroxylamine and Cr(III) was preconcentrated on a column of immobilised ferron on alumina. The adsorbed analyte was then eluted with 5?mL of hydrochloric acid and was determined by flame atomic absorption spectrometery. The speciation of chromium was affected by first passing the solution through an acidic alumina column which retained Cr(VI) and then Cr(III) was preconcentrated by immobilised ferron column and determined by FAAS. The concentration of Cr(VI) was determined from the difference of concentration of total chromium and Cr(III). The effect of pH, concentration of eluent, flow rate of sample and eluent solution, and foreign ions on the sorption of chromium (III) by immobilised ferron column was investigated. Under the optimised conditions the calibration curve was linear over the range of 2–400?µg?L^?1 for 1000?mL preconcentration volume. The detection limit was 0.32?µg?L^?1, the preconcentration factor was 400, and the relative standard deviation (%RSD) was 1.9% (at 10?µg?L^?1; n?=?7). The method was successfully applied to the determination of chromium species in water samples and total chromium in standard alloys.     

Hilbertian spatial periodically correlated first order autoregressive models

In this article, we consider Hilbertian spatial periodically correlated autoregressive models. Such a spatial model assumes periodicity in its autocorrelation function. Plausibly, it explains spatial functional data resulted from phenomena with periodic structures, as geological, atmospheric, meteorological and oceanographic data. Our studies on these models include model building, existence, time domain moving average representation, least square parameter estimation and prediction based on the autoregressive structured past data. We also fit a model of this type to a real data of invisible infrared satellite images.