Description Usage Arguments Details Value See Also Examples

Calculate a solution path of the organic lasso estimate (of error standard deviation) with a list of tuning parameter values. In particular, this function solves the squared-lasso problems and returns the objective function values as estimates of the error variance:
*\tilde{σ}^2_{λ} = \min_{β} ||y - X β||_2^2 / n + 2 λ ||β||_1^2.*

1 2 | ```
olasso_path(x, y, lambda = NULL, nlam = 100, flmin = 0.01,
thresh = 1e-08, intercept = TRUE)
``` |

`x` |
An |

`y` |
A response vector of size |

`lambda` |
A user specified list of tuning parameter. Default to be NULL, and the program will compute its own |

`nlam` |
The number of |

`flmin` |
The ratio of the smallest and the largest values in |

`thresh` |
Threshold value for underlying optimization algorithm to claim convergence. Default to be |

`intercept` |
Indicator of whether intercept should be fitted. Default to be |

This package also includes the outputs of the naive and the degree-of-freedom adjusted estimates, in analogy to `nlasso_path`

.

A list object containing:

`n`

and`p`

:The dimension of the problem.

`lambda`

:The path of tuning parameter used.

`a0`

:Estimate of intercept. A vector of length

`nlam`

.`beta`

:Matrix of estimates of the regression coefficients, in the original scale. The matrix is of size

`p`

by`nlam`

. The`j`

-th column represents the estimate of coefficient corresponding to the`j`

-th tuning parameter in`lambda`

.`sig_obj_path`

:Organic lasso estimates of the error standard deviation. A vector of length

`nlam`

.`sig_naive`

:Naive estimate of the error standard deviation based on the squared-lasso regression. A vector of length

`nlam`

.`sig_df`

:Degree-of-freedom adjusted estimate of the error standard deviation, based on the squared-lasso regression. A vector of length

`nlam`

.`type`

:whether the output is of a natural or an organic lasso.

1 2 3 | ```
set.seed(123)
sim <- make_sparse_model(n = 50, p = 200, alpha = 0.6, rho = 0.6, snr = 2, nsim = 1)
ol_path <- olasso_path(x = sim$x, y = sim$y[, 1])
``` |

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