| Type: | Package |
| Title: | Doubly Debiased Lasso (DDL) |
| Version: | 1.0.2 |
| Description: | Statistical inference for the regression coefficients in high-dimensional linear models with hidden confounders. The Doubly Debiased Lasso method was proposed in <doi:10.48550/arXiv.2004.03758>. |
| License: | MIT + file LICENSE |
| Encoding: | UTF-8 |
| Imports: | stats, glmnet, Matrix |
| RoxygenNote: | 7.1.2 |
| NeedsCompilation: | no |
| Packaged: | 2023-04-09 15:04:23 UTC; zhuyuqi |
| Author: | Domagoj Ćevid [aut], Chengzhu Huang [aut], Zijian Guo [aut, cre], Peter Bühlmann [aut] |
| Maintainer: | Zijian Guo <zijguo@stat.rutgers.edu> |
| Repository: | CRAN |
| Date/Publication: | 2023-04-09 15:20:01 UTC |
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 |
Y |
the outcome vector, of length |
index |
the vector of indexes for the regression coefficient of interest |
rho |
the trim level for |
rhop |
the trim level for |
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)
Computing confidence intervals
Description
generic function
Usage
ci(x, alpha = 0.05, alternative = c("two.sided", "less", "greater"))
Arguments
x |
An object of class |
alpha |
alpha Level of significance to construct confidence interval |
alternative |
indicates the alternative hypothesis to construct confidence interval and must be one of "two.sided" (default), "less", or "greater". |
Examples
index = 1
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)
# default alpha is 0.05
ci(result, alpha = 0.05)
ci(result, alpha = 0.05, alternative = "less")
ci(result, alpha = 0.05, alternative = "greater")
Computing confidence intervals
Description
'ci' method for class 'DDL'
Usage
## S3 method for class 'DDL'
ci(x, alpha = 0.05, alternative = c("two.sided", "less", "greater"))
Arguments
x |
An object of class 'DDL' |
alpha |
alpha Level of significance to construct confidence interval |
alternative |
indicates the alternative hypothesis to construct confidence interval and must be one of "two.sided" (default), "less", or "greater". |
Examples
index = 1
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)
# default alpha is 0.05
ci(result, alpha = 0.05)
ci(result, alpha = 0.05, alternative = "less")
ci(result, alpha = 0.05, alternative = "greater")
Summarizing DDL
Description
'summary' method for class 'DDL'
Usage
## S3 method for class 'summary.DDL'
print(x, ...)
Arguments
x |
An object of class 'summary.DDL' |
... |
Ignored |
Summarizing DDL
Description
'summary' method for class 'DDL'
Usage
## S3 method for class 'DDL'
summary(object, ...)
Arguments
object |
An object of class 'DDL' |
... |
Ignored |
Value
The function 'summary.DDL' returns a list of summary statistics of DDL given 'DDL'
Examples
index = 1
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)