`ConfidenceBands.AbstractConfidenceBand`

— Type`AbstractConfidenceBand`

Supertype for all confidence bands.

`ConfidenceBands.BonferroniBand`

— Type`BonferroniBand <: PlugInConfidenceBand`

Confidence band with pointwise significance level adjusted by a Bonferroni correction for multiple hypotheses.

`ConfidenceBands.BootstrapConfidenceBand`

— Type`BootstrapConfidenceBand <: AbstractConfidenceBand`

Supertype for all confidence bands that require bootstrap draws of parameters of interest.

`ConfidenceBands.PlugInConfidenceBand`

— Type`PlugInConfidenceBand <: AbstractConfidenceBand`

Supertype for all plug-in confidence bands.

`ConfidenceBands.PointwiseBand`

— Type`PointwiseBand <: PlugInConfidenceBand`

Pointwise confidence intervals with critical values based on a normal distribution.

`ConfidenceBands.PointwiseCVBootBand`

— Type`PointwiseCVBootBand <: BootstrapConfidenceBand`

Pointwise bootstrap confidence intervals based on the quantile of t-statistics.

`ConfidenceBands.PointwiseQuantileBootBand`

— Type`PointwiseQuantileBootBand <: BootstrapConfidenceBand`

Efron's pointwise equal-tailed percentile bootstrap confidence intervals.

`ConfidenceBands.ProjectionBand`

— Type`ProjectionBand{T} <: PlugInConfidenceBand`

The smallest (rectangular) confidence band that contains the Wald confidence ellipsoid for parameters with a given dimension.

`ConfidenceBands.SidakBand`

— Type`SidakBand <: PlugInConfidenceBand`

Šidák band with exact asymptotic simultaneous coverage only for point estimators that are uncorrelated elementwise.

`ConfidenceBands.SuptBand`

— Type`SuptBand(nuncovered::Real=0; ndraw::Real=1_000_000)`

Return a `SuptBand`

instance that requires `ndraw`

random numbers for computation. Results tend to be more accurate with a larger value of `ndraw`

.

A positive value of `nuncovered`

allows generalized error rate control described by Montiel Olea and Plagborg-Møller (2019). Specifically, at most `nuncovered`

number of point estimates are allowed to be not covered by the confidence band when considering the coverage.

**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.

`ConfidenceBands.SuptBand`

— Type`SuptBand <: PlugInConfidenceBand`

Plug-in sup-t confidence band. Implementation follows Montiel Olea and Plagborg-Møller (2019) Algorithm 1 and may allow generalized error rate control.

Critical values computed for `SuptBand`

are based on random draws from a normal distribution. Since the random numbers are drawn only once and stored in an unexported global object `_globalrandnpool`

, results from the same Julia session remain unchanged if executed multiple times. However, results obtained across different sessions are not identical because the random numbers generated vary. See Julia manual section on `Random`

for reproducibility of random numbers.

**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.

`ConfidenceBands.SuptCVBootBand`

— Type`SuptCVBootBand <: BootstrapConfidenceBand`

Critical-value-based bootstrap implementation of sup-t confidence band. Implementation follows Montiel Olea and Plagborg-Møller (2019) Algorithm 3 in appendix and may allow generalized error rate control.

**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.

`ConfidenceBands.SuptQuantileBootBand`

— Type`SuptQuantileBootBand <: BootstrapConfidenceBand`

Quantile-based bootstrap implementation of sup-t confidence band. Implementation follows Montiel Olea and Plagborg-Møller (2019) Algorithm 2 and may allow generalized error rate control.

**References**

`ConfidenceBands.criticalvalue`

— Method`criticalvalue(cb::PlugInConfidenceBand, level::Real, Σ::AbstractMatrix)`

Return the critical value for `cb`

with confidence level `level`

when the estimates have an estimated variance-covariance matrix `Σ`

. For some types of plug-in confidence bands, providing the number of point estimates in place of `Σ`

is sufficient.

`ConfidenceBands.pwcoverage`

— Method`pwcoverage(lb::AbstractVector, ub::AbstractVector, draws::AbstractMatrix)`

Compute the share of point estimates in bootstrap `draws`

that are covered by the corresponding confidence intervals with lower bounds `lb`

and upper bounds `ub`

for each parameter separately. See also `simulcoverage`

.

`ConfidenceBands.simulcoverage`

— Function`simulcoverage(lb::AbstractVector, ub::AbstractVector, draws::AbstractMatrix, nuncovered=0)`

Compute the share of point estimates in bootstrap `draws`

that are simultaneously covered by the confidence band with lower bound `lb`

and upper bound `ub`

, except for at most `nuncovered`

parameters. See also `pwcoverage`

.

`StatsAPI.confint`

— Method`confint(cb::PlugInConfidenceBand, θ::AbstractVector, Σ::AbstractMatrix; level::Real=0.9)`

Compute the specified plug-in confidence band with confidence level `level`

using point estiamtes `θ`

and variance-covariance matrix `Σ`

.

`StatsAPI.confint`

— Method`confint(cb::PlugInConfidenceBand, m::StatisticalModel; level::Real=0.9)`

Compute the specified plug-in confidence band with confidence level `level`

for the coefficients of model `m`

.

`StatsAPI.confint`

— Method`confint(cb::SuptCVBootBand, θ0::AbstractVector, draws::AbstractMatrix; level::Real=0.9)`

Compute a sup-t confidence band with critical-value-based bootstrap implementation based on Montiel Olea and Plagborg-Møller (2019) Algorithm 3 in appendix. `θ0`

is a vector of point estimates to be used as the middle points of the band. The bootstrap `draws`

of point estimates need to be in a matrix with each column being a vector of point estimates from the same draw. In addition to the lower and upper bounds, the critical value is returned as the third object.

**References**

`StatsAPI.confint`

— Method`confint(cb::SuptQuantileBootBand, draws::AbstractMatrix; level::Real=0.9, kwargs...)`

Compute a sup-t confidence band with quantile-based bootstrap implementation based on Montiel Olea and Plagborg-Møller (2019) Algorithm 2. The bootstrap `draws`

of point estimates need to be in a matrix with each column being a vector of point estimates from the same draw. In addition to the lower and upper bounds, the pointwise confidence level (when the intervals from the confidence band are viewed as pointwise confidence intervals) is returned as the third object.

The procedure involves solving a root-finding problem for seeking the band with the specified confidence level. This is accomplished with the `find_zero`

function from `Roots.jl`

. The default bracketing interval (or starting point) used to solve this problem can be overriden by specifying the keyword argument `x0`

. A solver from `Roots.jl`

can be specified with keyword argument `solver`

. Any additional keyword argument will be passed to `find_zero`

.

**References**