lla {penalizedcdf}

LLA approximation for CDF penalty

Description

Linearly approximate a part of the objective function to greatly speed up computations.

Usage

lla(b.o,
    lmb.rho,
    bm_gm,
    nu,
    nstep.lla = 100L,
    eps.lla = 1E-6)

Arguments

b.o

Vector of sparse-solution.

lmb.rho

Lambda-rho ratio.

bm_gm

Vector of pseudo-solution

nu

Shape parameter of the penalty.

nstep.lla

Maximum number of iterations of the LLA-algorithm (if used).

eps.lla

Convergence threshhold of the LLA-algorithm (if used).

Details

The LLA approximation allows the computationally intensive part to be treated as a weighted LASSO (Tibshirani, 1996) problem. In this way the computational effort is significantly less while maintaining satisfactory accuracy of the results. See Zou and Li (2008).

Value

b

Vector of the estimated sparse-solution.

Conv

Convergence check (0 if converged).

nstep.lla

Number of iterations done.

References

Tibshirani, R. (1996). Regression shrinkage and selection via the lasso. Journal of the Royal Statistical Society: Series B (Methodological), 58(1):267–288.

Zou, H. and Li, R. (2008). One-step sparse estimates in nonconcave penalized likelihood models. Annals of statistics, 36(4):1509