M-quantile regression shrinkage and selection via the Lasso and Elastic Net to assess the effect of meteorology and traffic on air quality.

In this work, we intersect data on size-selected particulate matter (PM) with vehicular traffic counts and a comprehensive set of meteorological covariates to study the effect of traffic on air quality. To this end, we develop an M-quantile regression model with Lasso and Elastic Net penalizations. This allows (i) to identify the best proxy for vehicular traffic via model selection, (ii) to investigate the relationship between fine PM concentration and the covariates at different M-quantiles of the conditional response distribution, and (iii) to be robust to the presence of outliers. Heterogeneity in the data is accounted by fitting a B-spline on the effect of the day of the year. Analytic and bootstrap-based variance estimates of the regression coefficients are provided, together with a numerical evaluation of the proposed estimation procedure. Empirical results show that atmospheric stability is responsible for the most significant effect on fine PM concentration: this effect changes at different levels of the conditional response distribution and is relatively weaker on the tails. On the other hand, model selection allows to identify the best proxy for vehicular traffic whose effect remains essentially the same at different levels of the conditional response distribution.

Functional exploratory data analysis for high-resolution measurements of urban particulate matter.

In this work we propose the use of functional data analysis (FDA) to deal with a very large dataset of atmospheric aerosol size distribution resolved in both space and time. Data come from a mobile measurement platform in the town of Perugia (Central Italy). An OPC (Optical Particle Counter) is integrated on a cabin of the Minimetrò, an urban transportation system, that moves along a monorail on a line transect of the town. The OPC takes a sample of air every six seconds and counts the number of particles of urban aerosols with a diameter between 0.28 µm and 10 µm and classifies such particles into 21 size bins according to their diameter. Here, we adopt a 2D functional data representation for each of the 21 spatiotemporal series. In fact, space is unidimensional since it is measured as the distance on the monorail from the base station of the Minimetrò. FDA allows for a reduction of the dimensionality of each dataset and accounts for the high space-time resolution of the data. Functional cluster analysis is then performed to search for similarities among the 21 size channels in terms of their spatiotemporal pattern. Results provide a good classification of the 21 size bins into a relatively small number of groups (between three and four) according to the season of the year. Groups including coarser particles have more similar patterns, while those including finer particles show a more different behavior according to the period of the year. Such features are consistent with the physics of atmospheric aerosol and the highlighted patterns provide a very useful ground for prospective model-based studies.

Robust small area prediction for counts.

A new semiparametric approach to model-based small area prediction for counts is proposed and used for estimating the average number of visits to physicians for Health Districts in Central Italy. The proposed small area predictor can be viewed as an outlier robust alternative to the more commonly used empirical plug-in predictor that is based on a Poisson generalized linear mixed model with Gaussian random effects. Results from the real data application and from a simulation experiment confirm that the proposed small area predictor has good robustness properties and in some cases can be more efficient than alternative small area approaches.

Semiparametric M-quantile regression for count data.

Lung cancer incidence over 2005-2010 for 326 Local Authority Districts in England is investigated by ecological regression. Motivated from mis-specification of a Negative Binomial additive model, a semiparametric Negative Binomial M-quantile regression model is introduced. The additive part relates to those univariate or bivariate smoothing components, which are included in the model to capture nonlinearities in the predictor or to account for spatial dependence. All such components are estimated using penalized splines. The results show the capability of the semiparametric Negative Binomial M-quantile regression model to handle data with a strong spatial structure.

Low-rank smoothing splines on complicated domains.

Smoothing over a domain with irregular boundaries or interior gaps and holes is addressed. Consider the problem of estimating mercury in sediment concentrations in the estuarine waters in New Hampshire. A modified version of low-rank thin plate splines (LTPS) is introduced where the geodesic distance is applied to evaluate dissimilarity of any two data observations: loosely speaking, distances between locations are not measured as the crow flies, but as the fish swims. The method is compared with competing smoothing techniques, LTPS, and finite element L-splines.