*! version 1.0.0 24jul2010

help rpecMichal Brzezinski (July 2010)

Title

rpec -- Estimate robustly the number (k) of extreme order statistics used for fitting the Pareto model to upper tails of distributions

Syntax

rpec [varname] [, options]

k(scalar) the maximum number of extreme order statistics used in estimation

x0(scalar) the minimum value of varname used in estimation

c(scalar) robustness constant

ns(scalar) number of Monte Carlo simulations

If neither k nor x0 options are used, nrpec searches for optimal k over the whole range of varname.

Description

rpec estimates the number k of extreme ordered statistics
(e.g. highest incomes) for fitting the Pareto model to the upper tail of the distribution.
It uses the robust Pareto error criterion (RC-criterion) introduced
in Dupuis and Victoria-Feser (2006).
Estimating k is equivalent to estimating the scale parameter x0 of the Pareto distribution:
k = SUM I(varname >= x0), where I is the indicator function. The estimated x0 can be then used in fitting Pareto model by, e.g., ML method, see paretofit.

For an implementation of non-robust Pareto error criterion for choosing k, also introduced in Dupuis and Victoria-Feser (2006), see nrpec, if installed.

Dependencies

rpec requires paretowml by Michal Brzezinski
and moremata by Ben Jann. First package is used to compute weighted
maximum likelihood estimator of Pareto distribution shape parameter.
It can be installed by typing net install paretowml,
from(http://coin.wne.uw.edu.pl/mbrzezinski/software/). The second package can
be installed by typing ssc install moremata.

Examples

To search for optimal k over the whole range of varname:

. rpec varname

To search for optimal k among the 50 largest values of varname

. rpec varname, k(50)

To search for optimal k among the values of varname >= 10000

. rpec varname, x0(10000)

References

Dupuis, Debbie J. and Victoria-Feser, Maria-Pia (2006). A Robust Prediction Error Criterion for Pareto Modelling of Upper Tails. The Canadian Journal of Statistics, 34 (4), 639-658.

Also see

Online: help for nrpec, paretofit, paretowml, paretoobre, hillp if installed.

Author

Michal Brzezinski <mbrzezinski@wne.uw.edu.pl>, Faculty of Economic Sciences, University of Warsaw, Poland.