Suppose x_1, x_2 lim x rightarrow Exp(theta) where x GE 0 and theta >0, that is
ID: 3158579 • Letter: S
Question
Suppose x_1, x_2 lim x rightarrow Exp(theta) where x GE 0 and theta >0, that is f(x) = 1/theta e^-t/theta Define T = x_1 Define S = x_1 + x_2 Define T^ = E|x_1|S Show that the V_at(T^) LE V_at(T) Show that S is a sufficient statistic for theta. At this point you have demonastrated that the Rao-Blackwell theorem value Recall the Rao-Blackwell theorem: Let X_1, X_2,...., X_n be a random sample from a distribution with PDF or PMF f(x, theta). Y_1 = u_1(X_1, X_2,..., X_n) be a sufficient statistic for theta Y_2 = u_2(X_1, X_2,..., X_n) be an unbalanced estimator of theta, where Y_1 is not a function of Y_1 alone. Thus, u(y_1) = E|Y_1|y_1| defines a statstic u(Y_1), a function of the sufficient statistic Y_1, which is an unbaised estimator of theta, and its variance is less than that of Y_2. Identify all of parts of the Rao-Blackwell Theorem.Explanation / Answer
solution:
In other words, a sufficient statistic T(X) for a parameter is a statistic such that the conditional distribution of the data X, given T(X), does not depend on the parameter .