Maximin: Returns a list that provides materials for later inference...

In MaximinInfer: Inference for Maximin Effects in High-Dimensional Settings

Returns a list that provides materials for later inference method.

Description

Given list of observations, compute the bias-corrected initial estimators and do bias-correction to the regressopm covariance matrix.

Usage

Maximin(
  Xlist,
  Ylist,
  loading.mat,
  X0 = NULL,
  cov.shift = TRUE,
  cov0 = NULL,
  intercept = TRUE,
  intercept.loading = FALSE,
  lambda = NULL,
  verbose = FALSE
)

Arguments

Xlist	list of design matrix for source data, of length L
Ylist	list of outcome vector for source data, of length L
loading.mat	Loading matrix, of dimension n.loading x p, each column corresponds to a loading of interest
X0	design matrix for target data, of dimension n0 x p (default = NULL)
cov.shift	Covariate shifts or not between source and target data (default = TRUE)
cov0	Covariance matrix for target data, of dimension p x p (default = NULL)
intercept	Should intercept be fitted for the initial estimator (default = TRUE)
intercept.loading	Should intercept term be included for the loading (default = FALSE)
lambda	The tuning parameter in fitting initial model. If NULL, it will be picked by cross-validation. (default = NULL)
verbose	Should intermediate message(s) be printed. (default = FALSE)

Details

The algorithm implemented scenarios with or without covariate shift. If cov0 is specified, the X0 will be ignored; if not, while X0 is specified, cov0 will be estimated by X0. If both are not specified, the algorithm will automatically set cov.shift as FALSE.

Value

The returned list contains the following components:

Gamma.plugin	The plugin regression covariance matrix
Gamma.debias	The proposed debiased regression covariance matrix
Var.Gamma	The variance matrix for sampling the regression covariance matrix
fits.info	The list of length L, that contains the initial coefficient estimators and variance of fitted residuals.
Points.info	The list of length L, that contains the initial debiased estimator for linear combinations and its corresponding standard error.

Examples

L = 2
n1 = n2 = 100; p = 4
X1 = MASS::mvrnorm(n1, rep(0,p), Sigma=diag(p))
X2 = MASS::mvrnorm(n2, rep(0,p), Sigma=0.5*diag(p))
b1 = seq(1,4)/10; b2 = rep(0.2, p)
y1 = as.vector(X1%*%b1+rnorm(n1)); y2 = as.vector(X2%*%b2+rnorm(n2))
loading1 = rep(0.4, p)
loading2 = c(-0.5, -0.5, rep(0,p-2))
loading.mat = cbind(loading1, loading2)
cov0 = diag(p)
mm = Maximin(list(X1,X2),list(y1,y2),loading.mat,cov0=cov0)

# inference
out = Infer(mm, gen.size=10)

MaximinInfer documentation built on April 12, 2023, 12:41 p.m.