PoSIAdjRSquared (version 0.1.0)

equal_tailed_interval: 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)

Value

L

lower bound

U

upper bound

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

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)