DISCUSSION : THE DANTZIG SELECTOR : STATISTICAL ESTIMATION WHEN p IS MUCH LARGER THAN
نویسندگان
چکیده
1. Introduction. This is a fascinating paper on an important topic: the choice of predictor variables in large-scale linear models. A previous paper in these pages attacked the same problem using the " LARS " algorithm (Efron, Hastie, Johnstone and Tibshirani [3]); actually three algorithms including the Lasso as middle case. There are tantalizing similarities between the Dantzig Selector (DS) and the LARS methods, but they are not the same and produce somewhat different models. We explore this relationship with the Lasso and LARS here.
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DISCUSSION : THE DANTZIG SELECTOR : STATISTICAL ESTIMATION WHEN p IS MUCH LARGER THAN
given just a single parameter t . Two active-set methods were described in [11], with some concern about efficiency if p were large, where X is n× p . Later when basis pursuit de-noising (BPDN) was introduced [2], the intention was to deal with p very large and to allow X to be a sparse matrix or a fast operator. A primal–dual interior method was used to solve the associated quadratic program, ...
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In many important statistical applications, the number of variables or parameters p is much larger than the number of observations n. Suppose then that we have observations y = Xβ + z, where β ∈ R is a parameter vector of interest, X is a data matrix with possibly far fewer rows than columns, n p, and the zi’s are i.i.d. N(0, σ). Is it possible to estimate β reliably based on the noisy data y? ...
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