Monotonicity conjecture for the efficiency of the maximum likelihood estimator
For each ρ>0\rho>0ρ>0, let Bρ=Eζρ2B_\rho=\mathbf{E}\zeta_\rho^2Bρ=Eζρ2, Mρ=Eξρ2M_\rho=\mathbf{E}\xi_\rho^2Mρ=Eξρ2, and Eρ=Bρ/MρE_\rho=B_\rho/M_\rhoEρ=Bρ/Mρ denote the efficiency of the maximum likelihood estimator. The lim…