7 problems

Mixture-based ME-estimator conjecture. For well-behaved mixing measures $\pi$, this estimator should be strongly consistent and relatively efficient. The conjecture concerns the th…

Criterion-function efficiency conjecture. Such criterion functions also result in consistent estimators, but the estimators make different statistical efficiency trade-offs, since…

Profile-over-extension efficiency conjecture. Profile-based marginalization is more efficient than extension-based marginalization in finite samples.

The tensor Curie–Weiss model and tensor Erdős–Rényi Ising models are considered, with the Hamiltonian scaled according to the underlying hypergraph model. Extension conjecture. Sim…

Consider conditional independence tests based on Azadkia–Chatterjee-type coefficients and conditional randomization tests, with local alternatives in which $\mX$ and $Y$ may be dep…

General lower-bound conjecture. The analogous asymptotic variance determined for the general model should constitute the general lower bound.

In a regular statistical model, first-, second-, third-, and fourth-order efficiency refer to successive orders in the asymptotic efficiency expansions of estimators. Ghosh's conje…