What is invariance of MLE?

What is invariance of MLE?

One of the most useful properties of the maximum likelihood estimator (MLE), often called the invariance property, is that if ˆθ is the MLE of θ, then h(ˆθ) is the MLE of h(θ). Many texts either define the MLE of h(θ) to be h(ˆθ), say that the property is immediate from the definition of the MLE, or quote Zehna (1966).

What is invariance property in statistics?

In statistics, the concept of being an invariant estimator is a criterion that can be used to compare the properties of different estimators for the same quantity. It is a way of formalising the idea that an estimator should have certain intuitively appealing qualities.

What is meant by invariance?

[ ĭn-vâr′ē-əns ] The property of remaining unchanged regardless of changes in the conditions of measurement. For example, the area of a surface remains unchanged if the surface is rotated in space; thus the area exhibits rotational invariance.

What is the best estimator?

Point estimation involves the use of sample data to calculate a single value (known as a statistic) which is to serve as a “best guess” or “best estimate” of an unknown (fixed or random) population parameter. More formally, it is the application of a point estimator to the data.

What is meant by Galilean invariance?

Galilean invariance is a cornerstone of classical mechanics. It states that for closed systems the equations of motion of the microscopic degrees of freedom do not change under Galilean transformations to different inertial frames.

Is the global maximum a maximum likelihood estimate?

Thus, finding the global maximum can be a major computational challenge. This class of estimators has an important invariance property. If ✓ˆ(x) is a maximum likelihood estimate for ✓, then g(✓ˆ(x)) is a maximum likelihood estimate for g(✓).

Is there a problem with the invariance property of Mle?

I have a problem with the invariance property of MLE who say: (cfr. Casella-Berger Statistical Inference) “If ˆθ is the MLE of the parametre θ and g( ⋅) is a 1 -to- 1 trasformation of θ, then ^ g(θ) = g(ˆθ) “.

Which is the maximum likelihood function for Casella Berger?

Casella-Berger Statistical Inference) “If ˆθ is the MLE of the parametre θ and g( ⋅) is a 1 -to- 1 trasformation of θ, then ^ g(θ) = g(ˆθ) “. My problem is that in the proof the book defines a new maximum likelihood function for g(θ):