aug_t: Augmented t-interval

In nisone: Inference for Samples of Size at Least One

Augmented t-interval

Description

Calculates a t-interval using augmented data c(x,A). The multiplier of this interval bounds the level above level, so these intervals are typically conservative. This method is very fast for n <= 100 and level %in% c(0.8, 0.9, 0.95, 0.99) because I saved those multipliers in an internal dataset. But it can be slow (on the order of a second) for other confidence levels or larger sample sizes.

Usage

aug_t(x, A = 0, level = 0.95, wt = 1)

Arguments

x	The vector of data
A	The prior mean
level	The level of the interval
wt	Weight for A. Don't touch this unless you know what you are doing.

Details

Suppose X_1,\ldots,X_n \sim N(\mu,\sigma^2). Suppose we have prior value A. This provides intervals of the form

\hat{\mu} \pm \eta \hat{\sigma}/\sqrt{n + 1},

where \hat{\mu} and \hat{\sigma} are the sample mean and sample standard deviation of the augmented data X_1,\ldots,X_n,A, and \eta is chosen large enough to maintain the confidence level at all parameter values.

The wt argument allows for more copies of A to be included in the data augmentation. But it doesn't work well with more data augmentation so you should not set it above 1. Though, you can set wt to be between 0 and 1 (to have less data augmentation) and this does seem to work pretty well, but I haven't studied it extensively, so use at your own risk.

Note that you have to choose A before seeing the data. If you choose it based on the data, then you no longer maintain the confidence level.

Value

The augmented t-interval of the specified level.

Author(s)

David Gerard

Examples

set.seed(1)
## A is exactly correct
x <- rnorm(10)
aug_t(x)
stats::t.test(x)$conf.int

## A is very wrong
x <- rnorm(10)
aug_t(x, A = 100)
stats::t.test(x)$conf.int

nisone documentation built on Sept. 8, 2026, 5:08 p.m.