Chapter 5

Point Estimation

5.1. Generalities

5.1.1. Definition – examples

Let images be a statistical model and let g be a map from Θ to a set A with a σ-algebra images.

DEFINITION 5.1.– An estimator of g(θ) is a measurable map from E to A.

In an estimation problem, the set of decisions is therefore the set where the function g of the parameter takes its values. It acts to, in light of the observations, admit a value for g(θ) (a “function of the parameter”).

COMMENT 5.1.– If the model is written in the form images, we may consider g to be a function of P.

EXAMPLE 5.1.– In all of the examples below, images.

1) images.

2) images.

3) images, where uθ denotes a uniform distribution on [0, θ], images; g(θ) = θ.

4) P = a set of distributions of the ...

Get Mathematical Statistics and Stochastic Processes now with O’Reilly online learning.

O’Reilly members experience live online training, plus books, videos, and digital content from 200+ publishers.