Explained: "The expected Fisher information Select one: a. depends..."

Barbara Schroder

Answered question

2021-11-30

The expected Fisher information
Select one:
a. depends uniquely on data.
b. depends uniquely on the parameter
c. depends uniquely on the sample size n
d. depends on both data and the parameter

Answer & Explanation

Anot1954

Beginner2021-12-01Added 16 answers

Step 1
Fishers information describes how much information about an unknown parameter we can get from a sample i.e., it measures the expected amount of information given by a random variable for a parameter.
Let the random variable be X and the unknown parameter is

θ

and the pdf is

f (x, θ)

and the sample size be n.
The fisher information is

= ∣ (θ) =

E {(\frac{δ}{δ θ} \log (f^{n} (x, θ)))}^{2}

Step 2
Hence from the above information we can say that the fisher information depends uniquely on the parameter.
Option a is incorrect as Fishers information does not depend uniquely on data.
Option b is the correct option as Fishers information depends uniquely on the parameter.
Option c is not correct because

I (θ)

depends on n but not uniquely.
Option d is incorrect as

I (θ)

depends uniquely on parameter only.

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