... ( Rao - Blackwell Theorem ) Suppose that X has a joint distribution depending on some unknown parameter 0 and that T = T ( X ) is a sufficient statistic for 0. ( Both 0 and T can be vector - valued . ) Let S S ( X ) be a statistic with Ee ...
... Rao - Blackwell Theorem , discovered by C. R. Rao and independently by Blackwell [ 6 ] in a form applicable to sequential problems , occupies a central position in the theory of estimation . The practical procedure of improving ...
... Rao- Blackwell theorem . Theorem 4 ( Rao - Blackwell ) . Assume that A is a convex subset of Rm and that L ( 0 , a ) is a convex function of a for all 0 € ✪ . Suppose also that T is a sufficient statistic for 0 , and that d ° ( x ) is ...
... Rao - Blackwell theorem , it suffices to restrict ourselves in the class of unbiased statistics of which are functions of T alone . By the unbiasedness of U and V , we have then E , U ( T ) = EV ( T ) θ , θ ε Ω ; equivalently , E。[ U ...
... Rao - Blackwell Theorem nor the Cramér - Rao inequal- ity may help in deciding whether an unbiased estimator W is the UMVUE of 7 ( 0 ) . An alternative approach is provided in this section . If the Rao - Blackwellized version in the end ...
... RAO–BLACKWELL THEOREM Theorem 5.4.7 Let X1 ,...,X n be a random sample with joint pf or pdf f(x1 ,...,x n ;θ) and let U = (U1 ,...,U n) be jointly sufficient for θ = (θ1 ,...,θ n). If T is any unbiased estimator of k (θ), and if T∗ = E ...
... Rao - Blackwell theorem says that an estimator should only depend on the sufficient statistic , otherwise it can be improved . Let R ( 0,0 ) = E。( 0 – 0 ) 2 denote the MSE of the estimator . 9.42 Theorem ( Rao - Blackwell ) . Let be an ...
... Rao—Blackwell Theorem Definition 3.23. A real-valued function f on a convex set C in R” is called convex if, for any at # y in C and any Ye (0, 1), f|Ya + (1 – ?)y s 5 f(x) + (1– )f(y). (3.2) The function f is strictly convex if (3.2) ...
... Rao - Blackwell Theorem . In some Russian texts the Rao - Blackwell Theorem is referred to as Kolmogorov - Rao - Blackwell Theorem . Let ( X , Y ) , i = 1 , 2 , n be i.i.d. bivariate discrete r.v. EXAMPLE 4.3.5 with p.m.f. given by f ...
... Rao - Blackwell theorem suggests that the search for estimators of q ( ) with low MSES can al- ways be restricted to an examination of functions of sufficient statistics , where hopefully the number of sufficient statistics required to ...