Results 1  10
of
38,467
Regression Shrinkage and Selection Via the Lasso
 JOURNAL OF THE ROYAL STATISTICAL SOCIETY, SERIES B
, 1994
"... We propose a new method for estimation in linear models. The "lasso" minimizes the residual sum of squares subject to the sum of the absolute value of the coefficients being less than a constant. Because of the nature of this constraint it tends to produce some coefficients that are exactl ..."
Abstract

Cited by 4212 (49 self)
 Add to MetaCart
We propose a new method for estimation in linear models. The "lasso" minimizes the residual sum of squares subject to the sum of the absolute value of the coefficients being less than a constant. Because of the nature of this constraint it tends to produce some coefficients
The adaptive LASSO and its oracle properties
 Journal of the American Statistical Association
"... The lasso is a popular technique for simultaneous estimation and variable selection. Lasso variable selection has been shown to be consistent under certain conditions. In this work we derive a necessary condition for the lasso variable selection to be consistent. Consequently, there exist certain sc ..."
Abstract

Cited by 683 (10 self)
 Add to MetaCart
The lasso is a popular technique for simultaneous estimation and variable selection. Lasso variable selection has been shown to be consistent under certain conditions. In this work we derive a necessary condition for the lasso variable selection to be consistent. Consequently, there exist certain
High dimensional graphs and variable selection with the Lasso
 ANNALS OF STATISTICS
, 2006
"... The pattern of zero entries in the inverse covariance matrix of a multivariate normal distribution corresponds to conditional independence restrictions between variables. Covariance selection aims at estimating those structural zeros from data. We show that neighborhood selection with the Lasso is a ..."
Abstract

Cited by 736 (22 self)
 Add to MetaCart
The pattern of zero entries in the inverse covariance matrix of a multivariate normal distribution corresponds to conditional independence restrictions between variables. Covariance selection aims at estimating those structural zeros from data. We show that neighborhood selection with the Lasso
The bayesian lasso
, 2005
"... The Lasso estimate for linear regression parameters can be interpreted as a Bayesian posterior mode estimate when the regression parameters have independent Laplace (doubleexponential) priors. Gibbs sampling from this posterior is possible using an expanded hierarchy with conjugate normal priors ..."
Abstract

Cited by 284 (0 self)
 Add to MetaCart
The Lasso estimate for linear regression parameters can be interpreted as a Bayesian posterior mode estimate when the regression parameters have independent Laplace (doubleexponential) priors. Gibbs sampling from this posterior is possible using an expanded hierarchy with conjugate normal priors
SIMULTANEOUS ANALYSIS OF LASSO AND DANTZIG SELECTOR
 SUBMITTED TO THE ANNALS OF STATISTICS
, 2007
"... We exhibit an approximate equivalence between the Lasso estimator and Dantzig selector. For both methods we derive parallel oracle inequalities for the prediction risk in the general nonparametric regression model, as well as bounds on the ℓp estimation loss for 1 ≤ p ≤ 2 in the linear model when th ..."
Abstract

Cited by 472 (11 self)
 Add to MetaCart
We exhibit an approximate equivalence between the Lasso estimator and Dantzig selector. For both methods we derive parallel oracle inequalities for the prediction risk in the general nonparametric regression model, as well as bounds on the ℓp estimation loss for 1 ≤ p ≤ 2 in the linear model when
Least angle regression
, 2004
"... The purpose of model selection algorithms such as All Subsets, Forward Selection and Backward Elimination is to choose a linear model on the basis of the same set of data to which the model will be applied. Typically we have available a large collection of possible covariates from which we hope to s ..."
Abstract

Cited by 1326 (37 self)
 Add to MetaCart
implements the Lasso, an attractive version of ordinary least squares that constrains the sum of the absolute regression coefficients; the LARS modification calculates all possible Lasso estimates for a given problem, using an order of magnitude less computer time than previous methods. (2) A different LARS
Estimation and Inference in Econometrics
, 1993
"... The astonishing increase in computer performance over the past two decades has made it possible for economists to base many statistical inferences on simulated, or bootstrap, distributions rather than on distributions obtained from asymptotic theory. In this paper, I review some of the basic ideas o ..."
Abstract

Cited by 1204 (4 self)
 Add to MetaCart
The astonishing increase in computer performance over the past two decades has made it possible for economists to base many statistical inferences on simulated, or bootstrap, distributions rather than on distributions obtained from asymptotic theory. In this paper, I review some of the basic ideas
The Dantzig selector: statistical estimation when p is much larger than n
, 2005
"... 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 p is a parameter vector of interest, A is a data matrix with possibly far fewer rows than columns, n ≪ ..."
Abstract

Cited by 879 (14 self)
 Add to MetaCart
≪ p, and the zi’s are i.i.d. N(0, σ 2). Is it possible to estimate x reliably based on the noisy data y? To estimate x, we introduce a new estimator—we call the Dantzig selector—which is solution to the ℓ1regularization problem min ˜x∈R p ‖˜x‖ℓ1 subject to ‖A T r‖ℓ ∞ ≤ (1 + t −1) √ 2 log p · σ
Convex Position Estimation in Wireless Sensor Networks
"... A method for estimating unknown node positions in a sensor network based exclusively on connectivityinduced constraints is described. Known peertopeer communication in the network is modeled as a set of geometric constraints on the node positions. The global solution of a feasibility problem fo ..."
Abstract

Cited by 493 (0 self)
 Add to MetaCart
for these constraints yields estimates for the unknown positions of the nodes in the network. Providing that the constraints are tight enough, simulation illustrates that this estimate becomes close to the actual node positions. Additionally, a method for placing rectangular bounds around the possible positions for all
Results 1  10
of
38,467