rqmcmb {rqmcmb2}R Documentation

Markov Chain Marginal Bootstrap for Quantile Regression

Description

MCMB for Quantile Regression (also see quantreg package by Roger Koenker)

Usage

rqmcmb(x=x, y=y, tau=0.5, K=100, int=TRUE,
plotTheta=FALSE)

Arguments

x a data matrix (n by p) for the design variables whose rows correspond to cases
y a response vector of length n
tau a percentile level between 0 and 1. Default at 0.5 for the median
K length of the MCMB sequence. Default is 100
plotTheta TRUE or FALSE for plotting the MCMB sequence. Default to FALSE
int should be set to TRUE if the intercept is to be included in the model, and to FALSE if no intercept is desired. Default is TRUE.

Value

A list with the following components:

coef the parameter estimate from rq()
theta a matrix containing the MCMB sequence. The first row is the initial parameter estimate from rq()
success returns 1 if MCMB is successful. A value of 0 indicates that the program fails to return a desired MCMB sequence
cn condition number of the X'X matrix.

WARNING

The MCMB may not be suitable for problems of small sample sizes. Severe collinearity in the x matrix could also be harmful.

Author(s)

Maria Kocherginsky (mkocherg@health.bsd.uchicago.edu) and Xuming He (x-he@uiuc.edu)

References

Kocherginsky, M., He, X. Extensions of the Markov Chain Marginal Bootstrap. Statistics & Probability Letters, in press.

Kocherginsky M, He X, Mu Y. (2005). Practical confidence intervals for regression quantiles. Journal of Computational and Graphical Statistics 14:41-55, 2005.

Kocherginsky, M. (2003). Extensions of the Markov Chain Marginal Bootstrap. Ph.D Thesis, University of Illinois Urbana-Champaign.

He, X. and Hu, F. (2002). Markov Chain Marginal Bootstrap. Journal of the American Statistical Association , Vol. 97, no. 459, 783-795.

See Also

rq

Examples

  library(quantreg)
  
  x <- cbind(rnorm(100), runif(100))
  y <- rnorm(100)

  #generate the MCMB sequence:
  mcmb <- rqmcmb(x, y, tau=.5, plotTheta=FALSE)

  #get MCMB estimates of mean, SD, and CI:
  rqmcmb.ci(mcmb)

  #plot the MCMB sequences:
  rqmcmb.plot(mcmb)
  


[Package rqmcmb2 version 1.0.2-1 Index]