Postinference.MHLS: Post-selection individual inference with lasso estimator

In seunghyunmin/EAlasso: Estimator Augmentation and Simulation-Based Inference

Description

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

Usage

postInference.MHLS(LassoEst, Ctype = "CI", X, Y, sig2.hat, tau = rep(1,
  ncol(X)), alpha = 0.05, MHsamples, target = which(LassoEst$B0 != 0),
  nChain = 10, method, niterPerChain = 500, parallel = FALSE,
  ncores = 2L, returnSamples = FALSE, ...)

Arguments

LassoEst	The result from lassoFit function with type="lasso".
Ctype	either "CI" or "CS" which represent confidence intervals and confidence sets, respectively. If "CI", confidence intervals for all active coefficients are generated. If "CS", target argument needs to be specified.
X	predictor matrix.
Y	response vector.
sig2.hat	variance of error term.
tau	numeric vector. Standard deviation of proposal distribution for each beta. Adjust the value to get relevant level of acceptance rate. Default is rep(1, ncol(X)).
alpha	confidence level for confidence interval.
MHsamples	optional argument. MHsamples from postInference.MHLS. If MHsamples is supplied, MH sampling step is omitted. See the example for the detail.
target	target active variables of which one wants to generate confidence set. Needs to be a subset of active set. See the example for the detail.
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 "coeff" or "mu".
niterPerChain	the number of iterations per chain.
parallel	logical. If parallel = TRUE, uses parallelization. Default is parallel = FALSE.
ncores	integer. The number of cores to use for parallelization.
returnSamples	logical. If returnSamples = TRUE, print Metropolis-Hastings samples. If MHsamples is supplied, returnSamples = FALSE is forced.
...	auxiliary MHLS arguments.

Details

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.

Value

MHsamples	a list of class MHLS.
confidenceInterval	(1-alpha) confidence interval for each active coefficient.

Examples

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)
LassoEst <- lassoFit(X = X, Y = Y, type = "lasso", lbd = lbd, weights = weights)
parallel <- (.Platform$OS.type != "windows")
P1 <- postInference.MHLS(LassoEst= LassoEst, X = X, Y = Y, sig2.hat = 1, alpha = .05,
nChain = 3, niterPerChain = 20, method = "coeff", parallel = parallel, returnSamples = TRUE)
P1
postInference.MHLS(LassoEst= LassoEst, MHsamples = P1$MHsamples,
                   Ctype = "CI", X = X, Y = Y, method = "coeff")
postInference.MHLS(LassoEst= LassoEst, MHsamples = P1$MHsamples,
                   Ctype = "CS", X = X, Y = Y, method = "coeff")

seunghyunmin/EAlasso documentation built on May 31, 2019, 8:31 a.m.