If we know the value of a sufficient statistic, but not the sample that generated it, am I right to suspect that the conditional distribution of any other statistic given the sufficient statistic will not depend on the parameter of interest?

balafiavatv

balafiavatv

Answered question

2022-08-10

If we know the value of a sufficient statistic, but not the sample that generated it, am I right to suspect that the conditional distribution of any other statistic given the sufficient statistic will not depend on the parameter of interest?

Answer & Explanation

Emely English

Emely English

Beginner2022-08-11Added 16 answers

That is correct, PROVIDED that the statistical model is right. But the sufficient statistic is not where you will find evidence that the model doesn't fit. For example, in estimating the mean and variance of a normally distributed population, the sufficient statistic is the pair whose components are the sum of the observations and the sum of their squares, whereas evidence of non-normality will be found in the residuals.

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