DDL {DDL}R Documentation

Point estimation and inference for a single regression coefficient in the high-dimensional linear model with hidden confounders.

Description

Computes the Doubly Debiased Lasso estimator of a single regression coefficient in the high-dimensional linear model with hidden confounders. It also constructs the confidence interval for the target regression coefficient.

Usage

DDL(X, Y, index, rho = 0.5, rhop = 0.5)

Arguments

X

the covariates matrix, of dimension n×pn\times p

Y

the outcome vector, of length nn

index

the vector of indexes for the regression coefficient of interest

rho

the trim level for XX, default is 0.5

rhop

the trim level for XjX_{-j}, default is 0.5

Value

index

the vector of indexes for the regression coefficient of interest

est_ddl

The vector of the Doubly Debiased Lasso estimator of the target regression coefficient

se

The vector of the standard error of the Doubly Debiased Lasso estimator

est_init

The vector of the spectral deconfounding estimator of the whole regression vector

Examples

index = c(1,2,10)
n=100
p=200
s=5
q=3
sigmaE=2
sigma=2
pert=1

H = pert*matrix(rnorm(n*q,mean=0,sd=1),n,q,byrow = TRUE)
Gamma = matrix(rnorm(q*p,mean=0,sd=1),q,p,byrow = TRUE)
#value of X independent from H
E = matrix(rnorm(n*p,mean=0,sd=sigmaE),n,p,byrow = TRUE)

#defined in eq. (2), high-dimensional measured covariates
X = E + H %*% Gamma

delta = matrix(rnorm(q*1,mean=0,sd=1),q,1,byrow = TRUE)

#px1 matrix, creates beta with 1s in the first s entries and the remaining p-s as 0s
beta = matrix(rep(c(1,0),times = c(s,p-s)),p,1,byrow = TRUE)

#nx1 matrix with values of mean 0 and SD of sigma, error in Y independent of X
nu = matrix(rnorm(n*1,mean=0,sd=sigma),n,1,byrow = TRUE)

#eq. (1), the response of the Structural Equation Model
Y = X %*% beta + H %*% delta + nu

result = DDL(X, Y, index)
summary(result)

[Package DDL version 1.0.2 Index]