individual.test: Identify nonzero individual-level partial correlations

Description

Identify nonzero individual-level partial correlations in time series data by controlling the rate of the false discovery proportion (FDP) exceeding \(c0\) at \(\alpha\), considering time dependence. Input an indEst class object returned by individual.est or population.est.

Usage

individual.test(
  indEst,
  alpha = 0.05,
  c0 = 0.1,
  targetSet = NULL,
  MBT = 3000,
  simplify = !is.null(targetSet)
)

Value

If simplify is FALSE, a \(p*p\) matrix with values 0 or 1 is returned. If the j-th row and k-th column of the matrix is 1, then the partial correlation coefficient between the j-th variable and the k-th variable is identified to be nonzero.

And if simplify is TRUE, a two-column matrix is returned, indicating the row index and the column index of recovered nonzero partial correlations. We only retain the results which the row index is less than the column index. Those with larger test statistics are sorted first.

Arguments

indEst: An indEst class object.
alpha: significance level, default value is 0.05.
c0: threshold of the exceedance rate of FDP, default value is 0.1. The choice of c0 depends on the empirical problem. A smaller value of c0 will reduce false positives, but it may also cost more false negatives.
targetSet: a two-column matrix. Each row contains two index corresponding to a pair of variables of interest. If NULL, any pair of two variables is considered to be of interest.
MBT: times of multiplier bootstrap, default value is 3000.
simplify: a logical indicating whether results should be simplified if possible.

References

Qiu Y. and Zhou X. (2021). Inference on multi-level partial correlations based on multi-subject time series data, Journal of the American Statistical Association, 00, 1-15.

Examples

Run this code

## Quick example for the individual-level inference
data(indsim)
# estimating partial correlation coefficients by scaled lasso
pc = individual.est(indsim)
# conducting hypothesis test
Res = individual.test(pc)