Mathematics – Statistics Theory
Scientific paper
2011-06-17
Mathematics
Statistics Theory
Scientific paper
Many methods have been developed to estimate the set of relevant variables in a sparse linear model Y= XB+e where the dimension p of B can be much higher than the length n of Y. Here we propose two new methods based on multiple hypotheses testing, either for ordered or non-ordered variables. Our procedures are inspired by the testing procedure proposed by Baraud et al (2003). The new procedures are proved to be powerful under some conditions on the data and their properties are non asymptotic. They gave better results in estimating the set of relevant variables than both the False Discovery Rate (FDR) and the Lasso, both in the common case (p
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