Analysis of PM10 air pollution in Brno based on a GLM with strongly rank-deficient design matrix

A family of complex (generalized) linear models has been suggested exhibiting strong rank-deficiency in the design matrix to allow for more precise modeling involving identification of significant air pollution sources, among others. From each of them the parameter estimates were obtained using both standard estimation procedure and a new sparse parameter estimation technique based on BPA4 - a four-step modification of the Basis Pursuit Algorithm originally suggested in [Chen {S. S.}, Donoho {D. L.}, Saunders {M. A.}. Atomic decomposition by basis pursuit.SIAM J. Sci. Comput., 20(1):33-61,1998.] for time-scale analysis of digital signals. The goal of the analysis was to identify the model and algorithm yielding most precise one-day forecasts of the level of pollution by PM10 with regard to the meteorological and seasonal covariates.