## ConfidenceBands.jl

Confidence bands for simultaneous statistical inference
Author junyuan-chen
Popularity
7 Stars
Updated Last
12 Months Ago
Started In
January 2023

# ConfidenceBands.jl

Confidence bands for simultaneous statistical inference

ConfidenceBands.jl is a lightweight Julia package for computing confidence bands that are useful for simultaneous statistical inference. In contrast to pointwise confidence intervals computed for each parameter separately, a confidence band treats the entire vector of parameters as a single object and is more suitable for comparisons involving multiple parameters.

## Example Usage

ConfidenceBands.jl extends the `confint` function for computing confidence bands. Accepted arguments may vary depending on the type of confidence band. Details may be found from docstrings in the help mode of Julia REPL.

#### Plug-In Confidence Bands

Computation of a plug-in confidence band is based on a critical value:

```using ConfidenceBands
# Compute the critical value for Bonferroni bands with 90% confidence level
# when there are five parameters
criticalvalue(BonferroniBand(), 0.9, 5)
# A variance-covariance matrix Σ is required for sup-t bands
criticalvalue(SuptBand(), 0.9, Σ)```

To obtain confidence bands:

```# First obtain point estimates θ as a vector and variance-covariance matrix Σ
lb, ub = confint(SuptBand(), θ, Σ, level=0.95)```

#### Bootstrap Confidence Bands

Some types of confidence bands are designed for a valid bootstrap sample provided by users. A bootstrap sample of point estimates needs to be collected in a matrix with each column being a vector of point estimates from the same draw. Currently, quantile-based and critical-value-based bootstrap implementation of sup-t bands (`SuptQuantileBootBand` and `SuptCVBootBand`) are implemented following Montiel Olea and Plagborg-Møller (2019):

```lb, ub, pwlevel = confint(SuptQuantileBootBand(), draws)
lb, ub, cv = confint(SuptCVBootBand(), θ, draws)```

The former additionally returns the confidence level when the intervals from the confidence band are viewed as pointwise confidence intervals. The latter additionally returns the critical value.

## References

Montiel Olea, José Luis and Mikkel Plagborg-Møller. 2019. "Simultaneous Confidence Bands: Theory, Implementation, and an Application to SVARs." Journal of Applied Econometrics 34 (1): 1-17.

### Used By Packages

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