gg: Gaussian mean estimation with Gaussian side information

In sdzhao/cole: COmpound Loss Emporium

Gaussian mean estimation with Gaussian side information

Description

Estimates the mean vector of a primary homoscedastic sequence of independent Gaussian observations under squared error loss by leveraging side information in the form of an auxiliary homoscedastic sequence of independent Gaussians. The optimal decision rule is estimated by directly minimizing an unbiased estimate of its risk.

Usage

gg(
  x1,
  s1,
  x2,
  s2,
  rho = 0,
  K = 10,
  C = 5,
  fast = TRUE,
  tol = 1e-05,
  maxit = 100,
  verbose = FALSE
)

Arguments

x1	primary Gaussian sequence
s1	standard deviation of primary sequence
x2	auxiliary Gaussian sequence of side information
s2	standard deviation of auxiliary sequence
rho	regularization parameter, closer to 0 means less regularization
K	number of grid points, in the interval [x_j1 - C s_1, x_j1 + C s1], over which to search for the jth tuning parameter, where C is define below
C	the value of the constant C in the interval above
fast	if TRUE, use the fast algorithm (may be numerically unstable if rho = 0)
tol	error tolerance for convergence of the unbiased risk estimate
maxit	maximum number of allowable iterations
verbose	should the value of SURE be reported at each iteration

Value

t1_hat	values of tuning parameters t1
t2_hat	values of tuning parameters t2
theta_hat	estimated values of means of primary Gaussian sequence

Examples

## generate data
n = 250
set.seed(1)
theta1 = rnorm(n)
theta2 = theta1
x1 = theta1 + rnorm(n)
x2 = theta2 + rnorm(n)
## loss of MLE
mean((theta1 - x1)^2)
## loss of estimator incorporating side information
mean((theta1 - gg(x1, 1, x2, 1)$theta_hat)^2)

sdzhao/cole documentation built on May 2, 2022, 9:42 a.m.