TML.noncensored: Truncated Maximum Likelihood Regression Without Censored Observations

Description

This function computes the truncated maximum likelihood regression estimate described in Marazzi and Yohai (2004). The error distribution is assumed to follow approximately a Gaussian or a log-Weibull distribution. The cut-off values for outlier rejection are fixed or adaptive.

Usage

TML.noncensored(formula, data, errors = "Gaussian", cu = NULL, 
                initial = "S",otp = "fixed", cov = "parametric", 
                input = NULL, control = list(), ...)

Value

TML.noncensored returns an object of class "TML". The function summary can be used to obtain or print a summary of the results. The generic extractor functions fitted, residuals and

weights can be used to extract various elements of the value returned by TML.noncensored. The function update can be used to update the model.

An object of class "TML" is a list with the following components:

th0: Initial coefficient estimates (S or input).
v0: Initial scale (S or input).
nit0: Reached number of iteration in lmrob.S (available only if fastS is TRUE).
th1: Final coefficient estimates.
v1: Final scale (S or input).
nit1: Number of iterations reached by the IRLS algorithm for the final estimates.
tu,tl: Final cut-off values.
alpha: Estimated proportion of retained observations.
tn: Number of retained observations.
beta: Consistency constant for scale.
weights: Vector of weights (0 for rejected observations, 1 for retained observations).
COV: Covariance matrix of the final estimates (th1[1],...,th1[p],v1) (where p=ncol(X)).
residuals: The residuals, that is response minus fitted values.
fitted.values: The fitted mean values.
call: The matched call.
formula: The formula supplied.
terms: The terms object used.
data: The data argument.

Arguments

formula

A formula, i.e., a symbolic description of the model to be fit (cf. glm or lm).

data

An optional data frame containing the variables in the model. If not found in data, the variables are taken from environment(formula), typically the environment from which TML.noncensored is called.

errors

"Gaussian": the error distribution is assumed to be Gaussian.
"logWeibull" : the error distribution is assumed to be 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 coefficients is provided on output.
"parametric": a parametric estimate of the covariance matrix of the coefficients is provided (to be used when n is small).
"nonparametric": a nonparametric estimate of the covariance matrix of the coefficients 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 TML.noncensored.control.

...

If fastS=TRUE, parameters for lmrob.S. See the function lmrob.control (from the robustbase package) 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(D243)
     Cost <- D243$Cost                             # Cost (Swiss francs)
     LOS  <- D243$LOS                              # Length of stay (days)
     Adm  <- D243$Typadm; Adm <- (Adm==" Urg")*1   # Type of admission 
                                                   # (0=on notification, 1=Emergency)
     Ass  <- D243$Typass; Ass <- (Ass=="P"   )*1   # Type of insurance 
                                                   # (0=usual, 1=private)
     Age  <- D243$age                              # Age (years)
     Dst  <- D243$dest;   Dst <- (Dst=="DOMI")*1   # Destination 
                                                   # (1=Home, 0=another hospital)
     Sex  <- D243$Sexe;   Sex <- (Sex=="M"   )*1   # Sex (1=Male, 0=Female)

     # Truncated maximum likelihood regression with Gaussian errors

     z    <- TML.noncensored(log(Cost)~log(LOS)+Adm+Ass+Age+Dst+Sex,
              otp="adaptive",control=list(fastS=TRUE))

     summary(z)
     
     # Truncated maximum likelihood regression with log-Weibull errors

     w    <- TML.noncensored(log(Cost)~log(LOS)+Adm+Ass+Age+Dst+Sex,
             errors="logWeibull",otp="adaptive",control=list(fastS=TRUE))

     summary(w)
}