# How to check that a sample suits multi-dimensional uniform distribution?

I have a 3-dimensional sample $(X_k,Y_k,Z_k), k=1, \ldots, N$ which I suspect to be uniform on some parallelepiped in $R^3$ (i.e. a set of the form [a;b]X[c;d]X[e;f], where numbers a,b,c,d,e,f are unknown).

1. How should I estimate numbers a, b, c, d, e, f? Obviously I can try MLE, but then my estimates are biased. Does unbiased estimates exist?
2. How can I check that my sample is indeed uniform?
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