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.

Return test statistic

Return type of test statistic: "t", "z", "F", or "χ²"

Return p value

Return p value after multiple-hypothesis adjustment, if any

Return requested number of replications

Return actual number of replications, subject to enumeration of Rademacher draws

Return number of bootstrapping clusters in test

Return degrees of freedom of test

Return residual degrees of freedom of test

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.

Return parameter value with peak p value in test

Return confidence interval matrix from test, one row per disjoint piece

Return bootstrap distribution of statistic in bootstrap test

Return numerator of test statistic

Return denominator of test statistic

Return auxilliary weight matrix for wild bootstrap