individual.est {BrainCon}

Estimate individual-level partial correlation coefficients

Description

Estimate individual-level partial correlation coefficients in time series data with 1-\alpha confidence intervals. Note that these are confidence intervals for single parameters, not simultaneous confidence intervals.

Usage

individual.est(
  X,
  lambda = NULL,
  type = c("slasso", "lasso"),
  alpha = 0.05,
  ci = TRUE
)

Arguments

X

time series data of an individual which is a n*p numeric matrix, where n is the number of periods of time and p is the number of variables.

lambda

a penalty parameter of order \sqrt{\log(p)/n}. If NULL, \sqrt{2*2.01/n*\log(p*(\log(p))^{1.5}/n^{0.5})} is used in scaled lasso, and \sqrt{2*\log(p)/n} is used in lasso. Increasing the penalty parameter may lead to larger residuals in the node-wise regression, causing larger absolute values of estimates of partial correlation coefficients, which may cause more false positives in subsequent tests.

type

a character string representing the method of estimation. "slasso" means scaled lasso, and "lasso" means lasso. Default value is "slasso".

alpha

significance level, default value is 0.05.

ci

a logical indicating whether to compute 1-\alpha confidence interval, default value is TRUE.

Value

An indEst class object containing two or four components.

coef a p*p partial correlation coefficients matrix.

ci.lower a p*p numeric matrix containing the lower bound of 1-\alpha confidence interval, returned if ci is TRUE.

ci.upper a p*p numeric matrix containing the upper bound of 1-\alpha confidence interval, returned if ci is TRUE.

asym.ex a matrix measuring the asymptotic expansion of estimates, which will be used for multiple tests.

type regression type in estimation.

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.

Sun T. and Zhang C. (2012). Scaled Sparse Linear Regression, Biometrika, 99, 879–898.

Liu W. (2013). Gaussian Graphical Model Estimation With False Discovery Rate Control, The Annals of Statistics, 41, 2948–2978.

Ren Z., Sun T., Zhang C. and Zhou H. (2015). Asymptotic Normality and Optimalities in Estimation of Large Gaussian Graphical Models, The Annals of Statistics, 43, 991–1026.

See Also

population.est.

Examples

## Quick example for the individual-level estimates
data(indsim)
# estimating partial correlation coefficients by scaled lasso
pc = individual.est(indsim)