lmp {normalp}

Fitted linear model with exponential power distribution errors

Description

The function lmp is used to fit linear model. It can be used when the errors are distributed as an exponential power distribution.

Usage

lmp(formula, data, p)

Arguments

formula

A symbolic description of the model to be fitted.

data

An optional data frame containing the variables in the model. By default the variables are taken from the environment.

p

The shape parameter. If specified, this function estimates the parameter by using the L_p-norm method.

Details

To evaluate the coefficients of the linear model, lmp uses the maximum likelihood estimators. This function can give some problems if the number of regressors is too high.

Value

The function lmp returns an object of class "lmp" and "lm". The function summary print a summary of the results. The generic accessor functions coefficients, effects, fitted.values and residuals extract various useful features of the value returned by lmp. An object of class "lmp" is a list containing at least the following components:

coefficients

A named vector of coefficients.

residuals

The residuals, that is responses minus fitted values.

fitted.values

The fitted values.

rank

The numeric rank of the fitted linear model.

df.residual

The residual degrees of freedom computed as in lm.

call

The matched call.

terms

The terms object used.

p

Estimate of the shape parameter computed on residuals.

knp

A logical parameter used by summary.

model

The model frame used.

iter

If its value is 1 we have had a difficult convergence.

Author(s)

Angelo M. Mineo

References

Mineo, A.M. (1995) Stima dei parametri di regressione lineare semplice quando gli errori seguono una distribuzione normale di ordine p (p incognito). Annali della Facolt\‘a di Economia dell’Universit\'a di Palermo (Area Statistico-Matematica), pp. 161-186.

Examples

e<-rnormp(n=100,mu=0,sigmap=4,p=3,method="d")
x<-runif(100)
y<-0.5+2*x+e
lmp(y~x)