wildboottest([T::DataType=Float64,] R::AbstractMatrix, r::AbstractVector; resp, <optional keyword arguments>) -> WildBootTests.BootTestResult

Function to perform wild-bootstrap-based hypothesis test

Positional arguments

• T::DataType: data type for inputs, results, and computations: Float32 or Float64 (default)
• R::AbstractMatrix and r::AbstractVector: required matrix and vector expressing the null Rβ=r; see notes below

Required keyword argument

• resp::AbstractVector: response/dependent variable (y or y₁ in Roodman et al. (2019))

Optional keyword arguments

• predexog::AbstractVecOrMat: exogenous predictors, including constant term, if any (X/X₁)
• predendog::AbstractVecOrMat: endogenous predictors (Y₂)
• inst::AbstractVecOrMat: instruments (X₂)
• R1::AbstractMatrix and r1::AbstractVector: model constraints; same format as for R and r
• clustid::AbstractVecOrMat{<:Integer}: data vector/matrix of error and bootstrapping cluster identifiers; see notes
• nbootclustvar::Integer=size(clustid,2): number of bootstrap-clustering variables
• nerrclustvar::Integer=nbootclustvar: number of error-clustering variables
• issorted:Bool=false: time-saving flag: data matrices are already sorted by column types 2, then 3, then 1 (see notes)
• hetrobust::Bool=true: true unless errors are treated as iid
• feid::AbstractVector{<:Integer}: data vector for one-way fixed effect group identifier
• fedfadj::Integer: degrees of freedom that fixed effects (if any) consume; defaults to number of FEs
• obswt::AbstractVector=[]: observation weight vector; default is equal weighting
• fweights::Bool=false: true for frequency weights
• maxmatsize::Number: maximum size of auxilliary weight matrix (v), in gigabytes
• ptype::Symbol=:symmetric: p value type (:symmetric, :equaltail, :lower, :upper)
• bootstrapc::Bool=false: true to request bootstrap-c instead of bootstrap-t
• liml::Bool=false: true for LIML or Fuller LIML
• fuller::Number: Fuller LIML factor
• kappa::Number: fixed κ for k-class estimation
• arubin::Bool=false: true for Anderson-Rubin test
• small::Bool=true: true to multiply test statistics by G/(G-1) × N/(N-k), where G, N, k are number of clusters, observations, and predictors
• clusteradj::Bool=true: false to drop G/(G-1) factor
• clustermin::Bool=false`: for multiway clustering, true to base G/(G-1) factor for all clusterings ]on the smallest G across clusterings
• jk::Bool=false: true to base the bootstrap data-generating process on residuals jackknifed by bootstrap cluster
• scorebs::Bool=false: true for score bootstrap instead of wild bootstrap
• reps::Integer=999: number of bootstrap replications; reps = 0 requests classical Rao (or Wald) test if imposenull = true (or false)
• imposenull::Bool=true: true to impose null
• auxwttype::Symbol=:rademacher: auxilliary weight type (:rademacher, :mammen, :webb, :normal, :gamma)
• rng::AbstractRNG=MersenneTwister(): randon number generator
• level::Number=.95: significance level (0-1)
• rtol::Number=1e-3: tolerance for confidence set bound determination
• madjtype::Symbol=:none: multiple hypothesis adjustment (:none, :bonferroni, :sidak)
• nH0::Integer=1: number of hypotheses tested, including one being tested now
• ml::Bool=false: true for (nonlinear) ML estimation
• scores::AbstractVecOrMat: for ML, pre-computed scores
• beta::AbstractVector: for ML, parameter estimates
• A::AbstractMatrix: for ML, covariance estimates
• gridmin: vector of graph lower bounds; max length 2, missing/NaN entries ask wildboottest() to choose
• gridmax: vector of graph upper bounds; missing/NaN entries ask wildboottest() to choose
• gridpoints: vector of number of sampling points; missing/NaN entries ask wildboottest() to choose
• getdist::Bool=:false: whether to return bootstrapped distribution for t/z/F/χ² statistics; and their numerators
• getci::Bool=true: whether to return confidence interval
• getplot::Bool=getci: whether to generate plot data
• getauxweights::Bool=false: whether to save auxilliary weight matrix (v)

Notes

T, ptype, auxwttype, and madjtype may also be strings. Examples: "Float32" and "webb".

The columns of R in the statement of the null should correspond to those of the matrix [predexog predendog], where predendog is non-empty only in regressions with instruments.

Order the columns of clustid this way:

1. Variables only used to define bootstrapping clusters, as in the subcluster bootstrap.
2. Variables used to define both bootstrapping and error clusters.
3. Variables only used to define error clusters.

nbootclustvar is then the number of columns of type 1 or 2; nerrclustvar is the number of columns of type 2 or 3. Typically clustid is a single column of type 2 and nbootclustvar and nerrclustvar default to 1.

wildboottest() does not handle missing data values: all data and identifier matrices must be restricted to the estimation sample.

teststat(::WildBootTests.BootTestResult{T}) -> T

Given a wildboottest() return object, extract test statistic

stattype(::WildBootTests.BootTestResult{T}) -> String

Given a wildboottest() return object, extract type of test statistic: "t", "z", "F", or "χ²"

p(::WildBootTests.BootTestResult{T}) -> T

Given a wildboottest() return object, extract p value

padj(::WildBootTests.BootTestResult{T}) -> T

Given a wildboottest() return object, extract p value after multiple-hypothesis adjustment, if any

reps(::WildBootTests.BootTestResult{T}) -> Int64

Given a wildboottest() return object, extract number of replications

repsfeas(::WildBootTests.BootTestResult{T}) -> Int64

Given a wildboottest() return object, extract actual number of replications, subject to enumeration of Rademacher draws

nbootclust(::WildBootTests.BootTestResult{T}) -> Int64

Given a wildboottest() return object, extract number of bootstrapping clusters in test

dof(::WildBootTests.BootTestResult{T}) -> Int64

Given a wildboottest() return object, extract degrees of freedom of test

dof_r(::WildBootTests.BootTestResult{T}) -> Int64

Given a wildboottest() return object, extract residual degrees of freedom of test

plotpoints(::WildBootTests.BootTestResult{T}) -> NamedTuple{(:X, :p), Tuple{Tuple{Vararg{Vector{T}, N} where N},Vector{T}}}

Return data for confidence plot of test. Return value is a 2-tuple with named entries X and p holding the confidence sampling locations and p values respectively. X is in turn a 1- or 2-tuple of vectors of sampling coordinates for each dimension of the tested hypothesis.

peak(::WildBootTests.BootTestResult{T}) -> NamedTuple{(:X, :p), Tuple{Vector{T}, T}}

Given a wildboottest() return object for a one-dimensional test, return the parameter value with peak p value in test Return value is a 2-tuple with named entries X and p holding the parameter value and p value.

ci(::WildBootTests.BootTestResult{T}) -> Matrix{T}

Given a wildboottest() return object for a one-dimensional test, extract the confidence interval(s) for test, one row per disjoint piece

dist(::WildBootTests.BootTestResult{T}) -> Matrix{T}

Given a wildboottest() return object, extract bootstrap distribution of statistic

statnumer(::WildBootTests.BootTestResult{T}) -> T

Given a wildboottest() return object, extract numerator of test statistic

statvar(::WildBootTests.BootTestResult{T}) -> T

Given a wildboottest() return object, extract squared denominator of test statistic

auxweights(::WildBootTests.BootTestResult{T}) -> Matrix{T}

Given a wildboottest() return object for a one-dimensional test, extract auxilliary weight matrix