ABSTRACT
A sequence of estimates {θ̃ n } of a parameter θ ∊ Θ is said to be weakly consistent (resp. strongly consistent) for θ ∊ Θ if for every θ ∊ Θ, https://www.w3.org/1998/Math/MathML"> θ ˜ n → P θ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315136288/c12c5089-77f8-4e14-84a1-364a5e26ae30/content/eq822.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> (resp. https://www.w3.org/1998/Math/MathML"> θ ˜ n → a .s . θ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315136288/c12c5089-77f8-4e14-84a1-364a5e26ae30/content/eq823.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> ) when θ is the true value of the parameter. In this section, we show that under fairly general conditions, the maximum-likelihood estimates are strongly consistent as the sample size tends to infinity.
