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How do you show that a statistic is complete?
Definition: A statistic T is called complete if E[g(T)]=0 for all and some function g implies that P(g(T)=0)=1 for all.
How do you find minimal sufficient statistics?
A sufficient statistic T : X T is minimal sufficient if for any sufficient statistic U : X U there is a measurable function g : UT such that T = g(U) ex|(· |)-a.s. for all .
How do you calculate sufficient statistics?
It is easy to see that if f(t) is a one to one function and T is a sufficient statistic, then f(T) is a sufficient statistic. In particular, we can multiply a sufficient statistic by a nonzero constant and get another sufficient statistic.
How do you read a sufficient statistic?
Sufficiency pertains to data reduction, not merely estimation. A sufficient statistic need not estimate anything. For example, if X1,In are did samples drawn from an exponential distribution with unknown mean, then X is sufficient for, but so is (X1++Xn1,In).
Are the calculated means sufficient in explaining the data?
x is a sufficient statistic if it retains all the information about the population mean that was contained in the original data points. According to statistician Ronald Fisher, no other statistic that can be calculated from the same sample provides any additional information as to the value of the parameter.
Is sufficient statistic unique?
The minimal sufficient statistic is not unique. But, the minimal sufficient partition is unique. {1+(yo )2}. The ratio is a constant function of if T(Y n)=(Y(1), ×··, Y(n)).
Does a minimal sufficient statistic always exist?
If there exists a minimal sufficient statistic, and this is usually the case, then every complete sufficient statistic is necessarily minimal sufficient(note that this statement does not exclude the option of a pathological case in which a complete sufficient exists while there is no minimal sufficient statistic).
Is a complete statistic sufficient?
(Base's Lemma) If T(X) is complete and sufficient (for ), and S(X) is ancillary, then S(X) and T(X) are independent for all . In other words, a complete sufficient statistic is independent of any ancillary statistic.
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