# Robust version of Hotelling $T^2$ test

I am looking for a robust version of Hotelling's $T^2$ test for the mean of a vector. As data, I have a $m\ \times\ n$ matrix, $X$, each row an i.i.d. sample of an $n$-dimensional RV, $x$. The null hypothesis I wish to test is $E[x] = \mu$, where $\mu$ is a fixed $n$-dimensional vector. The classical Hotelling test appears to be susceptible to non-normality in the distribution of $x$ (just as the 1-d analogue, the Student t-test is susceptible to skew and kurtosis).

what is the state of the art robust version of this test? I am looking for something relatively fast and conceptually simple. There was a paper in COMPSTAT 2008 on the topic, but I do not have access to the proceedings. Any help?

• thanks for editing to have proper math. I couldn't find info on how to render math in 'markdown' language. looks just like raw \LaTeX does it? – shabbychef Aug 6 '10 at 21:33
• Yes, it is Latex. See this meta thread: meta.stats.stackexchange.com/questions/218/… – user28 Aug 6 '10 at 21:46