LF: Inference for linear combination of the regression vector in...

In prabrishar1/SIHR: Statistical Inference in High Dimensional Regression

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,
  alpha = 0.05,
  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)
alpha	Level of significance to construct two-sided confidence interval (default = 0.05)
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
ci.mat	The matrix of two.sided confidence interval for the linear combination, of dimension ncol(loading.mat) x 2; each row 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)

prabrishar1/SIHR documentation built on April 17, 2023, 7:46 p.m.