ttest.TFM: T-test for Truncated Factor Model

In TFM: Sparse Online Principal Component for Truncated Factor Model

T-test for Truncated Factor Model

Description

This function performs a simple t-test for each variable in the dataset of a truncated factor model and calculates the False Discovery Rate (FDR) and power.

Usage

ttest.TFM(X, p, alpha = 0.05)

Arguments

X	A matrix or data frame of simulated or observed data from a truncated factor model.
p	The number of variables (columns) in the dataset.
alpha	The significance level for the t-test.

Value

A list containing:

FDR	The False Discovery Rate calculated from the rejected hypotheses.
Power	The power of the test, representing the proportion of true positives among the non-zero hypotheses.
pValues	A numeric vector of p-values obtained from the t-tests for each variable.
RejectedHypotheses	A logical vector indicating which hypotheses were rejected based on the specified significance level.

Examples

library(MASS)
library(mvtnorm)
set.seed(100)
p <- 400 
n <- 120 
K <- 5   
true_non_zero <- 100
B <- matrix(rnorm(p * K), nrow = p, ncol = K)
FX <- MASS::mvrnorm(n, rep(0, K), diag(K))
U <- mvtnorm::rmvt(n, df = 3, sigma = diag(p))
mu <- c(rep(1, true_non_zero), rep(0, p - true_non_zero))
X <- rep(1, n) %*% t(mu) + FX %*% t(B) + U  # The observed data
results <- ttest.TFM(X, p, alpha = 0.05)
print(results)

TFM documentation built on June 9, 2025, 9:08 a.m.