5 problems

Let $C$ be a bivariate copula, that is, a distribution function on $[0,1]^2$ with uniform marginals. A copula is stochastically increasing when it satisfies the stochastic increasi…

Let $s:[-\frac{1}{2},1]\to[-1,1]$ be the upper bound constructed in the preceding theorem, and let $\rho$ and $\phi$ denote Spearman's rho and Spearman's footrule for copulas. Non-…

Unit-efficiency conjecture. The Pitman asymptotic relative efficiency of $T$ with respect to $S$ for the independence test will usually be

Critical-boundary conjecture. The quantity $\zeta_{n,M}$ is always the critical detection boundary of the proposed test, regardless of how fast $M$ grows to infinity with $n$: ther…

Deb et al.'s conjecture. Allowing the number of nearest neighbors to grow could potentially lead to information theoretically efficient estimators.