The concept of a minimal sufficient statistic, which captures nothing more than the essential. Is it true that any random variable X as above has a sufficient statistic?

propappeale00

propappeale00

Answered question

2022-10-18

The concept of a minimal sufficient statistic, which captures nothing more than the essential.
Is it true that any random variable X as above has a sufficient statistic?

Answer & Explanation

broeifl

broeifl

Beginner2022-10-19Added 11 answers

In a degenerate manner your sample ( X 1 , . . . , X n ) is always a sufficient statistic from Fisher's information perspective. T ( X ) is sufficient statistic for θ iff I θ ( T ( X ) ) = I θ ( X 1 , . . . , X n ).Thus for every parametric structure you can take the data points themselves as the sufficient statistic.

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