postInference.MHLS {EAinference}

Post-inference with lasso estimator

Description

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

Usage

postInference.MHLS(X, Y, lbd, weights = rep(1, ncol(X)), tau = rep(1,
  ncol(X)), sig2.hat, alpha = 0.05, nChain = 10, method,
  niterPerChain = 500, parallel = FALSE, ncores = 2L,
  returnSamples = FALSE, ...)

Arguments

X

predictor matrix.

Y

response vector.

lbd

penalty term of lasso. By letting this argument be "cv.1se" or "cv.min", users can have the cross-validated lambda that gives either minimum squared error or that is within 1 std error bound.

weights

weight vector with length equal to the number of coefficients. Default is rep(1, ncol(X)).

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)).

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 "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.

...

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)
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)