The goal of DLL is to implement the Decorrelated Local Linear estimator proposed in <arxiv:1907.12732>. It constructs the confidence interval for the derivative of the function of interest under the high-dimensional sparse additive model.
You can install the released version of DLL from CRAN with:
This is a basic example which shows you how to solve a common problem:
library(DLL) library(MASS) # 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 = 500 p = 500 # 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 = 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) #> [1] 1.316374 1.453369
point estimates
DLL.model$est #> f1 #> -0.5 1.258581 #> 0.25 1.659544
standard errors
DLL.model$est.se #> f1 #> -0.5 0.3911074 #> 0.25 0.4301377
confidence interval
DLL.model$CI #> $f1 #> lower upper #> -0.5 0.4920249 2.025138 #> 0.25 0.8164900 2.502599
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