gfiUltra {gfiUltra}

Generalized fiducial inference for ultrahigh-dimensional regression

Description

Generates the fiducial simulations of the parameters of a "large p - small n" regression model and returns the selected models with their probability.

Usage

gfiUltra(formula, data, nsims = 1000L, verbose = FALSE, gamma = 1, ...)

Arguments

formula

a formula describing the model

data

dataframe in which to search the variables of the model

nsims

number of fiducial simulations

verbose

whether to print the messages generated by the screening procedure

gamma

tuning parameter; for expert usage only

...

named arguments passed to SIS, such as penalty = "lasso"

Value

A list with two elements: the fiducial simulations in a matrix (fidSims) and a vector giving the probabilities of the selected models (models).

References

Randy C. S. Lai, Jan Hannig & Thomas C. M. Lee. Generalized Fiducial Inference for Ultrahigh-Dimensional Regression. Journal of the American Statistical Association, Volume 110, 2015 - Issue 510, 760-772. <doi:10.1080/01621459.2014.931237>

Examples

# data ####
set.seed(666L)
n <- 300L
p <- 1000L
X <- matrix(rnorm(n * p), nrow = n, ncol = p)
colnames(X) <- paste0("x", 1L:p)
beta <- c(4, 5, 6, 7, 8)
y <- X[, 1L:5L] %*% beta + rnorm(n, sd = 0.9)
dat <- cbind(y, as.data.frame(X))
# fiducial simulations ####
gfi <- gfiUltra(y ~ ., data = dat, nsims = 10000L)
# selected models
gfi$models
# fiducial confidence intervals
gfiConfInt(gfi)
# fiducial estimates
gfiEstimates(gfi)