What is difference between enough and sufficient?
As determiners the difference between enough and sufficient is that enough is sufficient; all that is required, needed, or appropriate while sufficient is the smallest amount needed.
What is a minimal sufficient statistic?
Definition 1 (Minimal Sufficiency). A sufficient statistic T is minimal if for every sufficient statistic T and for every x, y ∈ X, T(x) = T(y) whenever T (x) = T (y). In other words, T is a function of T (there exists f such that T(x) = f(T (x)) for any x ∈ X). 3-1. Page 2.
Is a sufficient statistic unbiased?
Any estimator of the form U = h(T) of a complete and sufficient statistic T is the unique unbiased estimator based on T of its expectation. Hence, if T is complete and sufficient, U = h(T) is the MVUE of its expectation.
What is the same meaning of sufficient?
sufficient, enough, adequate, competent mean being what is necessary or desirable. sufficient suggests a close meeting of a need.
Is sufficient and suffice the same?
As a verb suffice is to be enough or sufficient; to meet the need (of anything); to be equal to the end proposed; to be adequate.
Why are sufficient statistics useful?
A sufficient statistic summarizes all of the information in a sample about a chosen parameter. In layman’s terms, a sufficient statistic is your best bet for summarizing your data; You can use it even if you don’t know any of the actual values in the sample.
Is sufficient statistic unique?
Sufficient statistics are not unique: Any one-to-one transformation of a sufficient statistic is again a sufficient statistic.
Is minimal sufficient statistics complete?
A minimal sufficient statistic is not necessarily complete. In this example, X1,…,Xn is a random sample from uniform(θ,θ +1), θ ∈ 勿, and we showed that T = (X(1),X(n)) is the minimal sufficient statistic for θ.
Is a function of a sufficient statistic a sufficient statistic?
The function v can depend on θ, but can depend on the random sample only through the value of r(x1,··· ,xn). 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.
Is UMVUE unique?
1 Answer. Generally, an UMVUE is essentially unique. The estimator you provided is not an UMVUE though, indeed it is not even unbiased!! Notice that E[1−X]=1−E[X]=1−p provided that our random variable is a Bernoulli with parameter p.
Is UMVUE admissible?
The estimator is in fact inadmissible when a > 1 and dominated by max(δ(X),0). So we have seen that although we may be able to compute an UMVUE, this may not be a desirable decision rule. The two examples above shows that, even in simple cases, the UMVUE may be inadmissible.
What is the difference between sufficient and enough?
is that enough is sufficient; all that is required, needed, or appropriate while sufficient is the smallest amount needed. is sufficiently. equal to the end proposed; adequate to wants; enough; ample; competent; as,.
Which is an example of a sufficient statistic?
Just look at the form of an exponential family of distribution. The function of the data in the exponent is the sufficient statistic. The most obvious case is the sample mean for a normally distributed data with a known variance. The sample mean is a sufficient statistic for the population mean.
What does thou art the most sufficient mean?
‘Thou art the most sufficient (I’ll say for thee),Not to believe a thing.’; A sufficiency; a quantity which satisfies desire, is adequate to the want, or is equal to the power or ability; as, he had enough to do take care of himself. ‘And Esau said, I have enough, my brother.’;
What is the meaning of the word sufficiency?
A sufficiency; a quantity which satisfies desire, is adequate to the want, or is equal to the power or ability; as, he had enough to do take care of himself. ‘And Esau said, I have enough, my brother.’; An exclamation denoting sufficiency, being a shortened form of it is enough.