itses: Iterative Sparse Estimation

In AmiAhm/itses: Iterative Sparse Estimation

Description

Performs iterative sparse estimation of many normal means either using the soft threshold estimator or the hard-threshold estimator.

Usage

itses(
  y,
  method = "ST",
  m = 5,
  init.lambda = "median",
  max.length = 5e+06,
  minimization.method = "numeric",
  debug = FALSE,
  sd = NA,
  sparsity = NA,
  sparse.mad = TRUE,
  remove.zero = TRUE,
  tol = 1e-08,
  h = 0.4,
  ...
)

Arguments

y	A n vector of observations.
method	Estimator which will be used. Can be either "ST" (Soft-Threshold estimator) or "HT" (Hard-Threshold estimator). Defaults to "ST".
m	The number of iterative steps. Default is 5.
init.lambda	Initial threshold to start iterations at. Can be: numeric; "median"; "visu" (universal threshold); and "half-visu" (universal threshold divded by 2). Defaults to "median".
max.length	The maximum number of observations n. Ifn is above internal calculations will downsample y to be of max.length size. Defaults to 5e6.
minimization.method	The risk minimization method which will be used. Can be either "numeric" or "sampling". Default is "numeric".
debug	logical. Specify wether or not to print debug code from iterations.
sd	Standard deviation of y i.e. noise levels. If NA will estiamt e using specified MAD estimator. Default is NA.
sparsity	Sparsity of y if known. 0 < sparsity < 1, closer to 1 means highly sparse. Is used in noise estimation if sparse noise estimation is used. Default is NA.
sparse.mad	logical. If TRUE use sparsity in MAD noise estimation. Default is TRUE.
remove.zero	logical. Remove observation that are zero from noise estimatiom. Default is TRUE.
tol	A numeric that determines the sensitivity of threshold selection. Default is 1e-8, iteration will stop if change is less than set tol.
h	Parameter for deciding eligibility of sparsity measure. Default is 0.4, only used with SparseMAD estimator.
...	parameters passed to risk minmization methods.
b	number of samples to take. Default is 10.
k	number of thresholds to initially evaluate. Default is 10.
max_num_iters	maximum number of iterations with Newton's method or spline interpolations (depending on method used). Default is 10.

Details

Given Y = (Y1, Y2, …, Yn), such that:

Yi ~ N(θ i, σ2), 1 ≤ i ≤ n.

N(θ, σ2) denotes the normal distribution with means θ and variance σ2. The means are to be estimated. Variance is either known or to be estimated.

Means are either estimated using the soft-threhsold (ST) or the hard-threshold (HT) estimator. ITSES minimize expected square error loss under repeated sampling (risk).

Soft-threshold: \hat{θ}(x)= sign(x)(abs(x)-λ)(abs(x)>λ).

Hard-threshold: \hat{θ}(x)= x(abs(x)>λ).

Value

List object with iteration results.

AmiAhm/itses documentation built on Dec. 17, 2021, 8:47 a.m.