equal_tailed_interval {PoSIAdjRSquared} | R Documentation |
Equal tailed interval
Description
This function inverts a post-selection p-value to a confidence interval.
Usage
equal_tailed_interval(z_interval, etajTy, alpha, tn_mu, tn_sigma)
Arguments
z_interval |
The intervals of type "list" where the OLS estimator gets selected: can be obtained from function "solve_selection_event" |
etajTy |
The OLS estimator of the j'th selected coefficient in the selected model of type "matrix" and dimension 1x1 |
alpha |
Integer for the desired significance level of the confidence interval |
tn_mu |
Integer for the mean of the truncated sampling distribution of the test statistic under the null hypothesis: for example, if you want to test beta_j=0, specify 0 for the mean |
tn_sigma |
Integer for the variance of the truncated sampling distribution of the test statistic |
Value
L |
lower bound |
U |
upper bound |
References
Pirenne, S. and Claeskens, G. (2024). Exact Post-Selection Inference for Adjusted R Squared.
Examples
# Generate data
n <- 100
Data <- datagen.norm(seed = 7, n, p = 10, rho = 0, beta_vec = c(1,0.5,0,0.5,0,0,0,0,0,0))
X <- Data$X
y <- Data$y
# Select model
result <- fit_all_subset_linear_models(y, X, intercept=FALSE)
phat <- result$phat
X_M_phat <- result$X_M_phat
k <- result$k
R_M_phat <- result$R_M_phat
kappa_M_phat <- result$kappa_M_phat
R_M_k <- result$R_M_k
kappa_M_k <- result$kappa_M_k
# Estimate Sigma from residuals of full model
full_model <- lm(y ~ 0 + X)
sigma_hat <- sd(resid(full_model))
Sigma <- diag(n)*(sigma_hat)^2
# Construct test statistic
Construct_test <- construct_test_statistic(j = 5, X_M_phat, y, phat, Sigma, intercept=FALSE)
a <- Construct_test$a
b <- Construct_test$b
etaj <- Construct_test$etaj
etajTy <- Construct_test$etajTy
# Solve selection event
Solve <- solve_selection_event(a,b,R_M_k,kappa_M_k,R_M_phat,kappa_M_phat,k)
z_interval <- Solve$z_interval
# Post-selection confidence interval
tn_sigma <- sqrt((t(etaj)%*%Sigma)%*%etaj)
equal_tailed_interval(z_interval, etajTy, alpha = 0.05, tn_mu = 0, tn_sigma)
[Package PoSIAdjRSquared version 0.0.0.1 Index]