Rejoinder : the Dantzig Selector : Statistical Estimation When P Is Much Larger Than
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چکیده
First of all, we would like to thank all the discussants for their interest and comments, as well as for their thorough investigation. The comments all underlie the importance and timeliness of the topics discussed in our paper, namely, accurate statistical estimation in high dimensions. We would also like to thank the editors for this opportunity to comment briefly on a few issues raised in the discussions. Of special interest is the diversity of perspectives, which include theoretical, practical and computational issues. With this being said, there are two main points in the discussions that are quite recurrent:
منابع مشابه
REJOINDER : THE DANTZIG SELECTOR : STATISTICAL ESTIMATION WHEN p IS MUCH LARGER
First of all, we would like to thank all the discussants for their interest and comments, as well as for their thorough investigation. The comments all underlie the importance and timeliness of the topics discussed in our paper, namely, accurate statistical estimation in high dimensions. We would also like to thank the editors for this opportunity to comment briefly on a few issues raised in th...
متن کاملREJOINDER: THE DANTZIG SELECTOR: STATISTICAL ESTIMATION WHEN p IS MUCH LARGER THAN n BY EMMANUEL CANDÈS AND TERENCE TAO
First of all, we would like to thank all the discussants for their interest and comments, as well as for their thorough investigation. The comments all underlie the importance and timeliness of the topics discussed in our paper, namely, accurate statistical estimation in high dimensions. We would also like to thank the editors for this opportunity to comment briefly on a few issues raised in th...
متن کاملDISCUSSION : 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, ...
متن کاملDISCUSSION : THE DANTZIG SELECTOR : STATISTICAL ESTIMATION WHEN p IS MUCH LARGER THAN
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) ...
متن کاملThe Dantzig selector : statistical estimation when p is much larger than
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 = Ax+ z, where x ∈ R is a parameter vector of interest, A 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 x reliably based on the noisy data y? T...
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تاریخ انتشار 2007