Point estimation rule: given iid sample x from parametric family f(·|θ), estimate θ̂ = argmax_θ L(θ; x) = argmax_θ ∏ f(xᵢ|θ). Consistent and asymptotically efficient under regularity conditions.
Maximum-likelihood estimation
Related concepts
- Probability measure P
- Law of large numbers
- Statistical hypothesis testing
- Cramér-Rao lower bound
- MLE first-order optimality: d ln L/d theta = 0 at theta-hat; Fisher information
- Likelihood ratio: Λ = L(θ_1|x)/L(θ_0|x)
- GC-MS quantitation (SIM, MRM)
- Rietveld refinement
- DoE (Fisher 1935 + Box-Behnken)
- Schild regression: log(r−1) = log[B] − log K_B; slope = 1 defines competitive antagonism (pA_2)
- Maximum likelihood phylogeny
- Clinical trial phases
- LOD-score linkage-mapping framework
- Threshold traits (Roff-Falconer liability model)