Description Usage Arguments Details Value Examples

Provides confidence intervals for the set of active coefficients of lasso using Metropolis-Hastings sampler.

1 2 3 4 |

`X` |
predictor matrix. |

`Y` |
response vector. |

`lbd` |
penalty term of lasso. By letting this argument be |

`weights` |
weight vector with length equal to the number of coefficients.
Default is |

`tau` |
numeric vector. Standard deviation of proposal distribution
for each beta. Adjust the value to get relevant level of acceptance rate.
Default is |

`sig2.hat` |
variance of error term. |

`alpha` |
confidence level for confidence interval. |

`nChain` |
the number of chains. For each chain, different plug-in beta will be generated from its confidence region. |

`method` |
Type of robust method. Users can choose either |

`niterPerChain` |
the number of iterations per chain. |

`parallel` |
logical. If |

`ncores` |
integer. The number of cores to use for parallelization. |

`returnSamples` |
logical. If |

`...` |
auxiliary |

This function provides post-selection inference for the active coefficients selected by lasso.
Uses Metropolis-Hastings sampler with multiple chains to draw from the
distribution under a fixed active set and generates `(1-alpha)`

confidence interval for each active coefficients.
Set `returnSamples = TRUE`

to check the Metropolis-Hastings samples.
Check the acceptance rate and adjust `tau`

accordingly.
We recommend to set `nChain >= 10`

and `niterPerChain >= 500`

.

`MHsamples` |
a list of class MHLS. |

`confidenceInterval` |
(1-alpha) confidence interval for each active coefficient. |

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 | ```
set.seed(123)
n <- 6
p <- 10
X <- matrix(rnorm(n*p),n)
Y <- X %*% rep(1,p) + rnorm(n)
sig2 <- 1
lbd <- .37
weights <- rep(1,p)
parallel <- (.Platform$OS.type != "windows")
postInference.MHLS(X = X, Y = Y, lbd = lbd, sig2.hat = 1, alpha = .05,
nChain = 3, niterPerChain = 20, method = "coeff", parallel = parallel)
postInference.MHLS(X = X, Y = Y, lbd = lbd, sig2.hat = 1, alpha = .05,
nChain = 3, niterPerChain = 20, method = "coeff", parallel = parallel, returnSamples = TRUE)
postInference.MHLS(X = X, Y = Y, lbd = lbd, sig2.hat = 1, alpha = .05,
nChain = 3, niterPerChain = 20, method = "mu", parallel = parallel)
postInference.MHLS(X = X, Y = Y, lbd = lbd, sig2.hat = 1, alpha = .05,
nChain = 3, niterPerChain = 20, method = "mu", parallel = parallel, returnSamples = TRUE)
``` |

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