Description
Non-Asymptotically Valid and Asymptotically Exact (NAVAE) Confidence Intervals.
Description
Implements the non-asymptotically valid and asymptotically exact confidence intervals in two cases: estimation of the mean, and estimation of (a linear combination of) the coefficients in a linear regression model, following (Derumigny, Girard and Guyonvarch, 2025) <doi:10.48550/arXiv.2507.16776>.
README.md
NAVAECI: Non-Asymptotically Valid and Asymptotically Exact (NAVAE) Confidence Intervals
Installation
You can install the development version of NAVAECI from GitHub with:
# install.packages("remotes")
remotes::install_github("AlexisDerumigny/NAVAECI")
Confidence interval for the mean
library(NAVAECI)
n = 4000
x = rexp(n, rate = 1/3) # so the mean is 3
Navae_ci_mean(x, bound_K = 9, alpha = 0.1)
#> Call: Navae_ci_mean(data = x, alpha = 0.1, bound_K = 9)
#>
#> CLT-based confidence interval:
#> 5 % 95 %
#> 2.946852 3.106489
#>
#> NAVAE confidence interval:
#> 5 % 95 %
#> 2.904051 3.149290
Confidence interval for the linear regression
n = 4000
X1 = rnorm(n, sd = 1)
true_eps = rnorm(n)
Y = 2 + 8 * X1 + true_eps
Navae_ci_ols(Y, X1, K_xi = 3, a = 1.1)
#> Call: Navae_ci_ols(Y = Y, X = X1, a = 1.1, K_xi = 3)
#>
#> CLT-based confidence intervals:
#> 2.5 % 97.5 % estimate length
#> intercept 1.962180 2.024766 1.993473 0.06258577
#> X1 7.987254 8.050967 8.019111 0.06371274
#>
#> NAVAE confidence intervals:
#> 2.5 % 97.5 % regime estimate length
#> intercept 1.717172 2.269774 Edg 1.993473 0.5526014
#> X1 7.742453 8.295769 Edg 8.019111 0.5533160