Sylvain Sardy, Université de Genève

Abstract:

We propose new test statistics based on lasso to test a null-hypothesis in generalized linear models. We show that under $H_0$ the test statistics are pivotal in the Gaussian case and asymptotically pivotal otherwise in the exponential family. With these new tests, the level is closer to the nominal level and the power is higher than existing tests in low and high dimension as well as for sparse and dense alternative hypotheses.