Within the framework of air quality monitoring in Normandy, we experiment the methods of sequential aggregation for forecasting concentrations of PM10 of the next day. Besides the field of application and the adaptation to the special context of the work of the forecaster, the main originality of this work is that the set of experts contains at the same time statistical models built by means of various methods and groups of predictors, as well as experts which are deterministic chemical models of prediction modeling pollution, weather and atmosphere. Numerical results on recent data from April 2013 until March 2015, on three monitoring stations, illustrate and compare various methods of aggregation. The obtained results show that such a strategy improves clearly the performances of the best expert both in errors and in alerts and reaches the “unbiasedness” of observed-forecasted scatterplot, which is especially difficult to obtain by usual methods. Joint work with Benjamin Auder (Univ. Paris-Sud Orsay, France), Michel Bobbia (Atmo Normandie, Rouen, France) and Bruno Portier (LMI., INSA Rouen, France). More details can be found in B. Auder, M. Bobbia, J-M. Poggi, B. Portier Sequential Aggregation of Heterogeneous Experts for PM10 Forecasting Atmospheric Pollution Research, 7, 1101-1109, 2016

# Seminario de Probabilidad y Estadística (2018)

Recent advances in Post-Selection Inference have shown that conditional testing is relevant and tractable in high-dimensions. In the Gaussian linear model, further works have derived unconditional test statistics such as the Kac-Rice Pivot for general penalized problems. In order to test the global null, a prominent offspring of this breakthrough is the spacing test that accounts the relative separation between the first two knots of the celebrated least-angle regression (LARS) algorithm. However, no results have been shown regarding the distribution of these test statistics under the alternative. For the first time, this paper addresses this important issue for the spacing test and shows that it is unconditionally unbiased. Furthermore, we provide the first extension of the spacing test to the frame of unknown noise variance. More precisely, we investigate the power of the spacing test for LARS and prove that it is unbiased: its power is always greater or equal to the significance level α. In particular, we describe the power of this test under various scenarii: we prove that its rejection region is optimal when the predictors are orthogonal; as the level α goes to zero, we show that the probability of getting a true positive is much greater than α; and we give a detailed description of its power in the case of two predictors. Moreover, we numerically investigate a comparison between the spacing test for LARS and the Pearson’s chi-squared test (goodness of fit). Generalisation to infinite dimensional Lasso is performed. Joint work with Yohann de Castro and Stéphane Mourareau