theorem ols_upward_bias {ρ covZε varZ : ℝ} (hcov : 0 < covZε) (hvar : 0 < varZ) : ρ < olsPlim ρ covZε varZ := by simp only [olsPlim, simultaneityBias] linarith [div_pos hcov hvar]
thesis/CESProofs/Foundations/CESEstimation.lean:218
CES Estimation Theory: Connecting Theory to Data