rqPen (version 4.1.3)

rq.nc.fit: Non-convex penalized quantile regression

Description

Warning: this function is no longer exported. Produces penalized quantile regression models for a range of lambdas and penalty of choice. If lambda is unselected than an iterative algorithm is used to find a maximum lambda such that the penalty is large enough to produce an intercept only model. Then range of lambdas goes from the maximum lambda found to "eps" on the log scale. Local linear approximation approach used by Wang, Wu and Li to extend LLA as proposed by Zou and Li (2008) to the quantile regression setting.

Usage

rq.nc.fit(
  x,
  y,
  tau = 0.5,
  lambda = NULL,
  weights = NULL,
  intercept = TRUE,
  penalty = "SCAD",
  a = 3.7,
  iterations = 1,
  converge_criteria = 1e-06,
  alg = "LP",
  penVars = NULL,
  internal = FALSE,
  ...
)

Value

Returns the following:

coefficients

Coefficients from the penalized model.

PenRho

Penalized objective function value. If scalex=TRUE then this is the value for the scaled version of x.

residuals

Residuals from the model.

rho

Objective function evaluation without the penalty.

coefficients

Coefficients from the penalized model.

tau

Conditional quantile being modeled.

n

Sample size.

penalty

Penalty used, SCAD or MCP.

penalty

Penalty selected.

Arguments

x

Matrix of predictors.

y

Vector of response values.

tau

Conditional quantile being modelled.

lambda

Vector of lambdas. Default is for lambdas to be automatically generated.

weights

Weights for the objective function.

intercept

Whether model should include an intercept. Constant does not need to be included in "x".

penalty

Type of penalty: "LASSO", "SCAD" or "MCP".

a

Additional tuning parameter for SCAD and MCP

iterations

Number of iterations to be done for iterative LLA algorithm.

converge_criteria

Difference in betas from iteration process that would satisfy convergence.

alg

Defaults for small p to linear programming (LP), see Wang, Wu and Li (2012) for details. QICD is no longer available.

penVars

Variables that should be penalized. With default value of NULL all variables are penalized.

internal

Whether call to this function has been made internally or not.

...

Additional items to be sent to rq.lasso.fit.

Author

Ben Sherwood, and Adam Maidman.

References

• Wang, L., Wu, Y. and Li, R. (2012). Quantile regression of analyzing heterogeneity in ultra-high dimension. J. Am. Statist. Ass, 107, 214--222.

• Wu, Y. and Liu, Y. (2009). Variable selection in quantile regression. Statistica Sinica, 19, 801--817.

• Zou, H. and Li, R. (2008). One-step sparse estimates in nonconcave penalized likelihood models. Ann. Statist., 36, 1509--1533.

• Peng, B. and Wang, L. (2015). An iterative coordinate-descent algorithm for high-dimensional nonconvex penalized quantile regression. J. Comp. Graph., 24, 676--694.

Examples

if (FALSE) {
x <- matrix(rnorm(800),nrow=100)
y <- 1 + x[,1] - 3*x[,5] + rnorm(100)
scadModel <- rq.nc.fit(x,y,lambda=1)
}