wtf1: Monotone Degree-One Weighted Trend Filter

In barbehenna/coleReg: COmpound Loss Emporium with Regression

Monotone Degree-One Weighted Trend Filter

Description

Estimate the mean of a homoscedastic sequence of independent Gaussian observations under squared error loss. The optimal separable estimator is estimated by minimizing an unbiased estimate of the risk under a monotone non-decreasing constraint. Under the monotonicity constraint, the unbiased risk estimate looks like a degree-one weighted trend filter.

Usage

wtf1(
  x,
  s,
  tau = TV1.oracle.plugin(x = x, s = s),
  M = ceiling(sqrt(length(x))),
  knots = NULL,
  backend = "CVXR",
  solver = "OSQP",
  ...
)

wtf1.cvxr(x, s, tau, knots = NULL, solver = "OSQP", ...)

wtf1.mosek(x, s, tau, knots = NULL)

Arguments

x	Gaussian sequence
s	standard deviation
tau	a scalar bound on TV(d')
M	number of evenly spaced knots (overrides knots if both specified)
knots	locations of knots
backend	one of "CVXR" or "MOSEK"
solver	solver backend for CVXR
...	additional parameters passed to CVXR::psolve() (if CVXR backend is used)

Details

The use of the MOSEK backend or solver required a properly installed 'Rmosek' package. The latest installation instructions found here: https://docs.mosek.com/latest/install/index.html and https://docs.mosek.com/latest/rmosek/install-interface.html.

The CVXR and MOSEK backends are designed for internal use only and do not validate inputs.

Value

theta_hat	estimated values of means of Gaussian sequence
x	original Gaussian sequence
s	known standard deviation
SURE	value of minimum risk estimate
tau	the user specified bound on TV(d')
TV1	the value of TV(d') for minimizer
intercept	intercept of fitted estimator
slopes	slopes of fitted estimator
knots	location of knots
backend	which version of wtf1 was used
solver	solver used by CVXR
...	additional inputed parameters

Examples

# basic usage
set.seed(1)
theta = rnorm(250)
x = theta + rnorm(250)
res = wtf1(x, s = 1, tau = 1.2, knots = -2:2)
mean((theta - res$theta_hat)^2)

barbehenna/coleReg documentation built on May 8, 2022, 12:05 a.m.