InvariantConditionalQuantilePrediction function

Invariant conditional quantile prediction.

Tests the null hypothesis that Y and E are independent given X.

InvariantConditionalQuantilePrediction(Y, E, X, alpha = 0.05,
  verbose = FALSE, test = fishersTestExceedance,
  mtry = sqrt(NCOL(X)), ntree = 100, nodesize = 5, maxnodes = NULL,
  quantiles = c(0.1, 0.5, 0.9), returnModel = FALSE)

Arguments

• Y: An n-dimensional vector.
• E: An n-dimensional vector. If test = fishersTestExceedance, E needs to be a factor.
• X: A matrix or dataframe with n rows and p columns.
• alpha: Significance level. Defaults to 0.05.
• verbose: If TRUE, intermediate output is provided. Defaults to FALSE.
• test: Unconditional independence test that tests whether exceedence is independent of E. Defaults to fishersTestExceedance.
• mtry: Random forest parameter: Number of variables randomly sampled as candidates at each split. Defaults to sqrt(NCOL(X)).
• ntree: Random forest parameter: Number of trees to grow. Defaults to 100.
• nodesize: Random forest parameter: Minimum size of terminal nodes. Defaults to 5.
• maxnodes: Random forest parameter: Maximum number of terminal nodes trees in the forest can have. Defaults to NULL.
• quantiles: Quantiles for which to test independence between exceedence and E. Defaults to c(0.1, 0.5, 0.9).
• returnModel: If TRUE, the fitted quantile regression forest model will be returned. Defaults to FALSE.

Returns

A list with the following entries:

• pvalue The p-value for the null hypothesis that Y and E are independent given X.
• model The fitted quantile regression forest model if returnModel = TRUE.

Examples

# Example 1
n <- 1000
E <- rbinom(n, size = 1, prob = 0.2)
X <- 4 + 2 * E + rnorm(n)
Y <- 3 * (X)^2 + rnorm(n)
InvariantConditionalQuantilePrediction(Y, as.factor(E), X)

# Example 2
E <- rbinom(n, size = 1, prob = 0.2)
X <- 4 + 2 * E + rnorm(n)
Y <- 3 * E + rnorm(n)
InvariantConditionalQuantilePrediction(Y, as.factor(E), X)