Dist: Inference for weighted quadratic functional of difference of...

In SIHR: Statistical Inference in High Dimensional Regression

Inference for weighted quadratic functional of difference of the regression vectors (excluding the intercept term) in high dimensional generalized linear regressions.

Description

Inference for weighted quadratic functional of difference of the regression vectors (excluding the intercept term) in high dimensional generalized linear regressions.

Usage

Dist(
  X1,
  y1,
  X2,
  y2,
  G,
  A = NULL,
  model = c("linear", "logistic", "logistic_alter"),
  intercept = TRUE,
  beta.init1 = NULL,
  beta.init2 = NULL,
  split = TRUE,
  lambda = NULL,
  mu = NULL,
  prob.filter = 0.05,
  rescale = 1.1,
  tau = c(0.25, 0.5, 1),
  alpha = 0.05,
  verbose = FALSE
)

Arguments

X1	Design matrix for the first sample, of dimension n_1 x p
y1	Outcome vector for the first sample, of length n_1
X2	Design matrix for the second sample, of dimension n_2 x p
y2	Outcome vector for the second sample, of length n_1
G	The set of indices, G in the quadratic form
A	The matrix A in the quadratic form, of dimension |G|\times|G|. If NULL A would be set as the |G|\times|G| submatrix of the population covariance matrix corresponding to the index set G (default = NULL)
model	The high dimensional regression model, either "linear" or "logistic" or "logistic_alter"
intercept	Should intercept(s) be fitted for the initial estimators (default = TRUE)
beta.init1	The initial estimator of the regression vector for the 1st data (default = NULL)
beta.init2	The initial estimator of the regression vector for the 2nd data (default = NULL)
split	Sampling splitting or not for computing the initial estimators. It take effects only when beta.init1 = NULL or beta.init2 = NULL. (default = TRUE)
lambda	The tuning parameter in fitting initial model. If NULL, it will be picked by cross-validation. (default = NULL)
mu	The dual tuning parameter used in the construction of the projection direction. If NULL it will be searched automatically. (default = NULL)
prob.filter	The threshold of estimated probabilities for filtering observations in logistic regression. (default = 0.05)
rescale	The factor to enlarge the standard error to account for the finite sample bias. (default = 1.1)
tau	The enlargement factor for asymptotic variance of the bias-corrected estimator to handle super-efficiency. It allows for a scalar or vector. (default = c(0.25,0.5, 1))
alpha	Level of significance to construct two-sided confidence interval (default = 0.05)
verbose	Should intermediate message(s) be printed. (default = FALSE)

Value

est.plugin	The plugin(biased) estimator for the quadratic form of the regression vectors restricted to G
est.debias	The bias-corrected estimator of the quadratic form of the regression vectors
se	Standard errors of the bias-corrected estimator, length of tau; corrsponding to different values of tau
ci.mat	The matrix of two.sided confidence interval for the quadratic form of the regression vector; row corresponds to different values of tau

Examples

X1 = matrix(rnorm(100*5), nrow=100, ncol=5)
y1 = -0.5 + X1[,1] * 0.5 + X1[,2] * 1 + rnorm(100)
X2 = matrix(rnorm(90*5), nrow=90, ncol=5)
y2 = -0.4 + X2[,1] * 0.48 + X2[,2] * 1.1 + rnorm(90)
G = c(1,2)
A = matrix(c(1.5, 0.8, 0.8, 1.5), nrow=2, ncol=2)
Est = Dist(X1, y1, X2, y2, G, A, model="linear")
Est$ci

SIHR documentation built on April 9, 2023, 5:08 p.m.