gg_rule: Separable rule for Gaussian mean estimation with Gaussian...

In sdzhao/cole: COmpound Loss Emporium

Separable rule for Gaussian mean estimation with Gaussian side information

Description

Given tuning parameter vectors t1 and t2, returns corresponding estimate for the mean vector of a primary homoscedastic sequence of independent Gaussian observations that leverages side information in the form of an auxiliary homoscedastic sequence of independent Gaussians.

Usage

gg_rule(x1, s1, x2, s2, t1, t2, r = 0, rho = 0)

Arguments

x1	primary Gaussian sequence
s1	standard deviation of primary sequence
x2	auxiliary Gaussian sequence of side information
s2	standard deviation of auxiliary sequence
t1	tuning parameter vector t1
t2	tuning parameter vector t2
r	correlation between x_i1 and x_i2, assuming they are bivariate normal
rho	regularization parameter, closer to 0 means less regularization

Value

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 oracle separable estimator
mean((theta1 - gg_rule(x1, 1, x2, 1, theta1, theta2))^2)

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