decode: Descent-based Calibrated Optimal Direct Estimation

In rDecode: Descent-Based Calibrated Optimal Direct Estimation

Description

Implement DECODE for sigma and beta to estimate Σ^-1β where sigma is an estimator of Σ and beta is an estimator of β.

Usage

decode(sigma, beta, lambda0, decode.tol = 1e-06, decode.maxit = 100,
  trace = FALSE, solver = c("apg", "homotopy"), solver.tol = 1e-08,
  solver.maxit = 10000, return.sigma = FALSE, return.beta = FALSE,
  return.param = FALSE)

Arguments

sigma	pxp positive semidefinite symmetric matrix. sigma will be perturbed if needed.
beta	p-length vector.
lambda0	number between 0 and 1.
decode.tol	error tolerance for DECODE.
decode.maxit	maximum iterations for DECODE
trace	logical. If TRUE, will return η, θ, and λ found during each iteration of DECODE
solver	solver for l1-RQP problem inside DECODE.
solver.tol	tolerance for solver.
solver.maxit	maximum iterations for solver (only for APG).
return.sigma	logical. If TRUE the sigma entered is returned.
return.beta	logical. If TRUE the beta entered is returned.
return.param	logical. If TRUE the parameters used are returned.

Value

An object of class decode containing:

eta	DECODE of Σ^-1β.
theta	final θ of the DECODE.
lambda	final λ of the DECODE.
sigma.mult	multiplier applied on sigma to ensure convergence.
total.iter	number of iterations until convergence.
call	the matched call.
method	the solver used, if requested.
lambda0	the lambda0 entered, if requested.
decode.tol	the decode.tol used, if requested.
decode.maxit	the decode.maxit used, if requested.
trace	the trace used, if requested.
solver.tol	the solver.tol used, if requested.
solver.maxit	the solver.maxit used, if requested.
eta.trace	matrix of η used in each iteration, if requested.
theta.trace	vector of θ used in each iteration, if requested.
lambda.trace	vector of λ used in each iteration, if requested.

References

Pun, C. S. (2018). A Sparse Learning Approach to Relative-Volatility-Managed Portfolio Selection. Hadimaja, M. Z., & Pun, C. S. (2018). A Self-Calibrated Regularized Direct Estimation for Graphical Selection and Discriminant Analysis.

Examples

# estimate A^(-1) b with a certain lambda0
X <- matrix(rnorm(100), 10, 10)
A <- t(X) %*% X
b <- rnorm(10)
object <- decode(A, b, lambda0 = 0.8)

object
summary(object)

coef(object)

rDecode documentation built on Dec. 18, 2019, 5:08 p.m.