AbstractConfidenceBand

Supertype for all confidence bands.

BonferroniBand <: PlugInConfidenceBand

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

BootstrapConfidenceBand <: AbstractConfidenceBand

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

PlugInConfidenceBand <: AbstractConfidenceBand

Supertype for all plug-in confidence bands.

PointwiseBand <: PlugInConfidenceBand

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

ProjectionBand{T} <: PlugInConfidenceBand

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

SidakBand <: PlugInConfidenceBand

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

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.

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.

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.

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

• 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.

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.

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.

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.

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 sample of point estimates draws is required to be 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

• 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.

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 sample of point estimates draws is required to be 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

• 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.