Method | Boosting Multiple Testing

Algorithm

Sequential variable admission

The candidate set is evaluated conditionally on the intercept, any always-in variables supplied through Xcond, and variables admitted in earlier iterations.

Initial ranking
Fit one auxiliary regression for each candidate and compute the absolute t- or z-statistic.
Initial admission
Admit the candidate with the largest finite statistic only when it exceeds the critical value based on delta1; otherwise stop with no selected candidates.
Conditional re-estimation
Recompute each remaining candidate statistic conditional on the variables already selected and the always-in set.
Stopping rule
Admit the strongest remaining candidate only when its statistic exceeds the critical value based on delta2; otherwise stop.

\[c_p(n,\delta_s)=\Phi^{-1}\!\left(1-\frac{p}{2n^{\delta_s}}\right),\qquad s\in\{1,2\}\]

Here n is the number of candidates still active at the current iteration. delta1 applies in the initial stage and delta2 in subsequent stages. If delta2 is omitted, it defaults to delta1.

The selection loop has no user-specified iteration limit. It stops when no remaining candidate crosses the applicable threshold or when no candidates remain.

Function reference

`boosting_glm()`

Usage

boosting_glm(
  y,
  X,
  Xcond = NULL,
  pval = 0.05,
  delta1 = 1,
  delta2 = delta1,
  link = c("linear", "logit", "probit"),
  HAC = FALSE
)

Argument	Role
y	Numeric response vector. Binary 0/1 values are expected for logit and probit models.
X	Numeric matrix whose columns are candidate regressors.
Xcond	Optional numeric matrix of controls that remain in every auxiliary regression.
pval	Probability level entering the multiple-testing critical value.
delta1	Critical-value exponent for the initial selection stage; the default is 1.
delta2	Critical-value exponent for subsequent stages; if omitted, it defaults to `delta1`.
link	One of `linear`, `logit`, or `probit`.
HAC	For linear, logit, and probit models, use Newey-West standard errors with automatic bandwidth selection when `TRUE`.

Return value. A logical vector of length ncol(X). Conditioning variables in Xcond are not included in this vector.

Inference

Conventional and HAC statistics

Default

HAC = FALSE uses conventional model-based coefficient standard errors.

Newey-West

HAC = TRUE replaces those standard errors with sandwich::NeweyWest() and automatic bandwidth selection.

The HAC option is available for linear, logit, and probit models.