LF {SIHR}

Inference for linear combination of the regression vector in high dimensional generalized linear regression

Description

Inference for linear combination of the regression vector in high dimensional generalized linear regression

Usage

LF(
  X,
  y,
  loading.mat,
  model = c("linear", "logistic", "logistic_alter"),
  intercept = TRUE,
  intercept.loading = FALSE,
  beta.init = NULL,
  lambda = NULL,
  mu = NULL,
  prob.filter = 0.05,
  rescale = 1.1,
  verbose = FALSE
)

Arguments

X

Design matrix, of dimension n x p

y

Outcome vector, of length n

loading.mat

Loading matrix, nrow=p, each column corresponds to a loading of interest

model

The high dimensional regression model, either "linear" or "logistic" or "logistic_alter"

intercept

Should intercept be fitted for the initial estimator (default = TRUE)

intercept.loading

Should intercept term be included for the loading (default = FALSE)

beta.init

The initial estimator of the regression vector (default = NULL)

lambda

The tuning parameter in fitting initial model. If NULL, it will be picked by cross-validation. (default = NULL)

mu

The dual tuning parameter used in the construction of the projection direction. If NULL it will be searched automatically. (default = NULL)

prob.filter

The threshold of estimated probabilities for filtering observations in logistic regression. (default = 0.05)

rescale

The factor to enlarge the standard error to account for the finite sample bias. (default = 1.1)

verbose

Should intermediate message(s) be printed. (default = FALSE)

Value

est.plugin.vec

The vector of plugin(biased) estimators for the linear combination of regression coefficients, length of ncol(loading.mat); each corresponding to a loading of interest

est.debias.vec

The vector of bias-corrected estimators for the linear combination of regression coefficients, length of ncol(loading.mat); each corresponding to a loading of interest

se.vec

The vector of standard errors of the bias-corrected estimators, length of ncol(loading.mat); each corresponding to a loading of interest

proj.mat

The matrix of projection directions; each column corresponding to a loading of interest.

Examples

X <- matrix(rnorm(100 * 5), nrow = 100, ncol = 5)
y <- -0.5 + X[, 1] * 0.5 + X[, 2] * 1 + rnorm(100)
loading1 <- c(1, 1, rep(0, 3))
loading2 <- c(-0.5, -1, rep(0, 3))
loading.mat <- cbind(loading1, loading2)
Est <- LF(X, y, loading.mat, model = "linear")

## compute confidence intervals
ci(Est, alpha = 0.05, alternative = "two.sided")

## summary statistics
summary(Est)