Description Usage Arguments Value See Also Examples

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

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

`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 the underlying optimization algorithm to claim convergence. Default to be |

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

`glmnet_output` |
Should the estimate be computed using a user-specified output from |

A list object containing:

`n`

and`p`

:The dimension of the problem.

`lambda`

:The path of tuning parameters used.

`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`

.`a0`

:Estimate of intercept. A vector of length

`nlam`

.`sig_obj_path`

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

`nlam`

.`sig_naive_path`

:Naive estimates of the error standard deviation based on lasso regression, i.e.,

*||y - X \hat{β}||_2 / √ n*. A vector of length`nlam`

.`sig_df_path`

:Degree-of-freedom adjusted estimate of standard deviation of the error. A vector of length

`nlam`

. See Reid, et, al (2016).`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)
nl_path <- nlasso_path(x = sim$x, y = sim$y[, 1])
``` |

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