ABSTRACT
The nature of what we are about to discuss is conceptually very different from anything we had included in previous chapters. So far, we developed methodologies from the point of view of a frequentist. So far, we have started with a random sample https://www.w3.org/1998/Math/MathML"> X 1 , … , X n https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429113741/fa82963e-6109-44c7-ad13-faec498214f4/content/eq7909.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> from a population having the probability mass function (pmf) or probability density function (pdf) https://www.w3.org/1998/Math/MathML"> f ( x ; ϑ ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429113741/fa82963e-6109-44c7-ad13-faec498214f4/content/eq7910.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> with https://www.w3.org/1998/Math/MathML"> x ∈ X https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429113741/fa82963e-6109-44c7-ad13-faec498214f4/content/eq7911.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> and https://www.w3.org/1998/Math/MathML"> ϑ ∈ Θ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429113741/fa82963e-6109-44c7-ad13-faec498214f4/content/eq7912.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> where we assumed that the unknown parameter https://www.w3.org/1998/Math/MathML"> ϑ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429113741/fa82963e-6109-44c7-ad13-faec498214f4/content/eq7913.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> was fixed. Thus, all inference procedures relied upon the likelihood function, https://www.w3.org/1998/Math/MathML"> L ( ϑ ) = ∏ i = 1 n f x i ; ϑ . https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429113741/fa82963e-6109-44c7-ad13-faec498214f4/content/eq7914.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/>
