estimate_nuisance_pc: The function for nuisance parameter estimation in simple_pc_testing() and debiased_pc_testing().

Description

The function for nuisance parameter estimation in simple_pc_testing() and debiased_pc_testing().

Usage

estimate_nuisance_pc(
  nuisance_sample_1,
  nuisance_sample_2 = NULL,
  pca_method = "sparse_pca",
  mean_method = "naive",
  num_latent_factor = 1,
  local_environment = NA
)

Value

A list of estimated nuisance quantities.

estimate_leading_pc: Leading principle components
estimate_mean_1: Sample mean for group 1
estimate_mean_2: Sample mean for group 1
estimate_eigenvalue: Eigenvalue for each principle compoenent.
estimate_noise_variance: Noise variance, I need this to construct block-diagonal estimates of the covariance matrix.

Arguments

nuisance_sample_1: Group 1 sample. Each row is a subject and each column corresponds to a feature.
nuisance_sample_2: Group 2 sample. Each row is a subject and each column corresponds to a feature.
pca_method: Methods used to estimate principle component The default is "sparse_pca", using sparse PCA from package PMA. Other choices are "dense_pca"---the regular PCA; and "hard"--- hard-thresholding PCA, which also induces sparsity.
mean_method: Methods used to estimate the mean vector. Default is sample mean "naive". There is also a hard-thresholding sparse estiamtor "hard".
num_latent_factor: Number of principle to be estimated/tested. Default is 1.
local_environment: A environment for hyperparameters shared between folds.