DLL {DLL} | R Documentation |
It constructs the Decorrelated Local Linear estimator and estimates its standard error. It further constructs the confidence interval for the derivative of the function of interest.
DLL(
X,
y,
D.ind,
d0,
h = NULL,
lam.seq = NULL,
treatment.SAM = FALSE,
data.swap = FALSE,
quant.trans = FALSE,
alpha = 0.05
)
X |
the covariates matrix, of dimension |
y |
the outcome vector, of length |
D.ind |
the column index(es) of X, indicating the index(es) of the variable(s) of interest. It can be a scalar or a vector. If vector, then do inference for each index of the sequence. |
d0 |
evaluation points for derivative estimation. It can be scalar or vector. |
h |
bandwidth, computed by Rule of Thumb from the package “locpol” if not provided. |
lam.seq |
a sequence of tuning parameters considered in fitting the sparse additive model. Cross validation is used to choose the best one. If not provided(default), the default sequence ranges from 5e-3 to 1 with the length of 100. If provided, the sequence needs to be in a decreasing order for the reason of computation efficiency. |
treatment.SAM |
Whether a sparse additive model is used for fitting the treatment model? If 'False'(default), Lasso with cross validation is used to fit the treatment model. Default is 'FALSE' |
data.swap |
Whether data swapping is conducted or not? Default is 'FALSE' |
quant.trans |
Whether quantile transformation is conducted or not? Default is 'FALSE' |
alpha |
the significance level. Default is 0.05 |
est |
point estimates of the function derivative |
est.se |
estimated standard errors of est |
CI |
list of lower and upper bounds of confidence intervals |
d0 |
evaluation points |
bw.save |
selected bandwidth at each element of d0 |
sigma1.sq |
estimated variance of the error term in the outcome model |
# evaluation points
d0 = c(-0.5,0.25)
f = function(x) 1.5*sin(x)
f.deriv = function(x) 1.5*cos(x)
g1 = function(x) 2*exp(-x/2)
g2 = function(x) (x-1)^2 - 25/12
g3 = function(x) x - 1/3
g4 = function(x) 0.75*x
g5 = function(x) 0.5*x
# sample size and dimension of X
n = 200
p = 100
# covariance structure of D and X
Cov_Matrix = toeplitz(c(1, 0.7, 0.5, 0.3, seq(0.1, 0, length.out = p-3)))
set.seed(123)
# X represents the (D,X) here
X = MASS::mvrnorm(n,rep(-0.25,p+1),Sigma = Cov_Matrix)
e = rnorm(n,sd=1)
# generating response
y = f(X[,1]) + g1(X[,2]) + g2(X[,3]) + g3(X[,4]) + g4(X[,5]) + g5(X[,6]) + e
### DLL inference
DLL.model = DLL(X=X, y=y, D.ind = 1, d0 = d0)
# true values
f.deriv(d0)
# point estimates
DLL.model$est
# standard errors
DLL.model$est.se
# confidence interval
DLL.model$CI