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TITLE: T-statistic based correlation and heterogeneity robust inference, with applications to risk, inequality and concentration measurement
SPEAKER: Rustam Ibragimov
ABSTRACT:
Many risk, inequality, poverty and concentration measures are extremely
sensitive to outliers, dependence, heterogeneity and heavy tails. In this
paper we focus on robust measurement of risk, inequality, poverty and
concentration under heterogeneity, dependence and heavy-tailedness
of largely unknown form using the recent results on t-statistic based
heterogeneity and correlation robust inference in Ibragimov and Muller
(2007). The robust large sample inference on risk, inequality, poverty and
concentration measures is conducted as follows: partition the observations
into q>=2 groups, calculate the empirical measures for each group and conduct
a standard test with the resulting q estimators of the population measures.
Numerical results confirm the appealing
properties of tstatistic based robust inference method in this context, and
its applicability to many widely used risk, inequality, poverty and
concentration measures, including Sharpe ratio; value at risk and expected
shortfall; Gini coecient; Theil index, mean logarithmic deviation and
generalized entropy measures; Atkinson measures; coecient of variation and
Herfindahl-Hirschman index; head count, poverty gap and squared poverty gap
indices and other Foster-Greer-Thorbecke measures of poverty, among others.
The results discussed in the paper further indicate a strong link
between the tstatistic based robust inference methods and stochastic
analogues of the majorization conditions that are usually imposed on risk,
inequality, poverty and concentration measures related to
self-normalized sums or their transforms, as in the case of Sharpe ratio,
coefficient of variation and Herndahl-Hirschman index.
