TML1.noncensored: Truncated Maximum Likelihood Estimates of Location and Scale

Description

This functions computes the truncated maximum likelihood estimates of location and scale described in Marazzi and Yohai (2004). It assumes that the error distribution is approximately Gaussian or log-Weibull. The cut-off values for outlier rejection are fixed or adaptive. This function is a simplified version of TML.noncensored for the case without covariates.

Usage

TML1.noncensored(y, errors= c("Gaussian", "logWeibull"), cu = NULL, 
     initial = c("S", "input"), otp = c("adaptive", "fixed"), 
     cov = c("no", "parametric", "nonparametric"), input = NULL, 
     control = list(), ...)

Value

A list with the following components:

th0: Initial location estimate (S or input).
v0: Initial scale estimate (S or input).
nit0: Reached number of iteration if initial="S"
th1: Final location estimate.
v1: Final scale estimate.
nit1: Reached iteration number in IRLS algorithm for final estimate (only for the log_Weibull case).
tu, tl: Final cut-off values.
alpha: Estimated proportion of retained observations.
tn: Number of retained observations.
beta: Consistency constant for scale.
wi: Vector of weights (0 for rejected observations, 1 for retained observations).
CV0: Covariance matrix of the initial estimates (th0,v0).
CV1: Covariance matrix of the final estimates (th1,v1).

Arguments

y

Observation vector

errors

"Gaussian": the error distribution is assumed to be approximately Gaussian.
"logWeibull" : the error distribution is assumed to be approximately log-Weibull.

cu

Preliminary minimal upper cut-off. The default is 2.5 in the Gaussian case and 1.855356 in the log-Weibull case.

initial

"S" : initial S-estimate.
"input" : the initial estimate is given on input.

otp

"adaptive": adaptive cut-off.
"fixed" : non adaptive cut-off.

cov

"no": no estimate of the covariance matrix of the estimates is provided on output.
"parametric": a parametric estimate of the covariance matrix of the location-scale estimates is provided (to be used when n is small).
"nonparametric": a nonparametric estimate of the covariance matrix of the location-scale estimates is provided.

input

Initial input estimates of location and scale.
Required when initial="input".

"Gaussian case" : list(theta=...,sigma=...) initial input estimates. theta: location; sigma: scale.
"logWeibull case" : list(tau=...,v=...) initial input estimates of location (tau) and scale (v).

control

Control parameters. For the default values, see the function TML1.noncensored.control.

...

If initial="S", parameters for the computation of the initial S estimates. See the function TML1.noncensored.control.S for the default values.

References

Marazzi A., Yohai V. (2004). Adaptively truncated maximum likelihood regression with asymmetric errors. Journal of Statistical Planning and Inference, 122, 271-291.

Examples

Run this code


if (FALSE) {
      data(Z243)
      Cost <- Z243$CouTot                         
      y    <- log(Cost)
      ctrl <- TML1.noncensored.control(iv=1,tol=1e-3)
      z    <- TML1.noncensored(y,errors="logWeibull", initial="S",otp="adaptive",
              cov="no",control=ctrl)
}