[Probabilidad-Estadistica-Seminario] Seminario de Probabilidad y Estadística -- Viernes 9 de marzo -- 10:30 horas

[Andrés Sosa]

Hola

Este *viernes 9 de marzo a las 10:30 horas* en el salón de seminarios del
Centro de Matemática hablará *Jean-Marc  Azaïs* (University of Toulouse )
en una sesión especial del seminario de Probabilidad y Estadística.

El título de la charla es: *Spacing test for the Lasso.*

Saludos.
Andrés




*Resumen: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*
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