Maximum Likelihood Estimation

1 General results. We consider a family of probability measures on X https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781351076777/1531b062-750f-426f-9035-7dcbd680db0f/content/eq514.tif"/> dominated by a σ-finite measure μ. The corresponding density functions are f(·, θ), θ ∈ Θ, where Θ is a set in R^k . We shall denote the likelihood function for a set of n observations by fⁿ , so that f n ( x 1 ,   x 2 ,   … ,   x n ,   θ ) =   ∏ r   =   1 n f ( x r ,   θ ) . https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781351076777/1531b062-750f-426f-9035-7dcbd680db0f/content/eq515.tif"/>