decode {rDecode}

Descent-based Calibrated Optimal Direct Estimation

Description

Implement DECODE for sigma and beta to estimate \Sigma^{-1}\beta where sigma is an estimator of \Sigma and beta is an estimator of \beta.

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

p \times p 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 \eta, \theta, and \lambda found during each iteration of DECODE

solver

solver for \ell_1-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 \Sigma^{-1}\beta.

theta

final \theta of the DECODE.

lambda

final \lambda 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 \eta used in each iteration, if requested.

theta.trace

vector of \theta used in each iteration, if requested.

lambda.trace

vector of \lambda 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)