The Dantzig Selector: Statistical Estimation When p Is Much Larger Than n The Dantzig selector is a new estimator introduced to estimate a parameter vector β in high-dimensional statistical settings where the number of variables p is much larger than the number of observations n. The estimator is derived from an ℓ₁-regularization problem that ensures the estimated vector is consistent with the noisy data. The method relies on the uniform uncertainty principle, which guarantees that the data matrix X has certain properties that allow for accurate estimation of β. The Dantzig selector achieves a loss within a logarithmic factor of the ideal mean squared error that would be achieved with perfect knowledge of the non-zero components of β. This makes it a powerful tool for variable selection in high-dimensional settings, as it can recover the best subset of variables by solving a simple convex program. The method is robust to noise and has been shown to perform well in various statistical applications, including biomedical imaging, signal processing, and genomics. The results are non-asymptotic and provide explicit constants for the error bounds. The Dantzig selector is particularly effective when the true parameter vector is sparse or compressible, and it has been shown to achieve the minimax rate for certain types of sparse parameters. The method is computationally tractable and can be implemented as a linear program, making it a practical solution for high-dimensional statistical estimation.The Dantzig Selector: Statistical Estimation When p Is Much Larger Than n The Dantzig selector is a new estimator introduced to estimate a parameter vector β in high-dimensional statistical settings where the number of variables p is much larger than the number of observations n. The estimator is derived from an ℓ₁-regularization problem that ensures the estimated vector is consistent with the noisy data. The method relies on the uniform uncertainty principle, which guarantees that the data matrix X has certain properties that allow for accurate estimation of β. The Dantzig selector achieves a loss within a logarithmic factor of the ideal mean squared error that would be achieved with perfect knowledge of the non-zero components of β. This makes it a powerful tool for variable selection in high-dimensional settings, as it can recover the best subset of variables by solving a simple convex program. The method is robust to noise and has been shown to perform well in various statistical applications, including biomedical imaging, signal processing, and genomics. The results are non-asymptotic and provide explicit constants for the error bounds. The Dantzig selector is particularly effective when the true parameter vector is sparse or compressible, and it has been shown to achieve the minimax rate for certain types of sparse parameters. The method is computationally tractable and can be implemented as a linear program, making it a practical solution for high-dimensional statistical estimation.