Use the MLE of and find its asymptotic distribution using the MLE-CLT.
Use the MLE of and find its asymptotic distribution using the MLE-CLT. (N, 0) (N, 0)
Let Xi iid∼ N(0, θ) for i = 1, ..., n. a) Find the MLE for θ. Call it b) Is biased? c) Is consistent? d) Find the variance of (e) What is the asymptotic distribution of ?
4. Let Xi" pois(1) for i = 1, ..., n. (a) Find the MLE for d. Call it û (b) What is the asymptotic distribution of î? (c) Find an estimator for P(X1 < 1) (hint: write down P(X1 < 1) using the distribution. Can you use a property of MLEs to get this? )
4.(120) Let X1,,,Xn be iid r(, 1) and g(u) given. Let 6n be the MLE of g(4) (1)(60) Find the asymptotic distribution of 6, (2)(60) Find the ARE of T Icc(X) w.r.t. on P(X1> c), c > 0 is i n i1 5.(80) Let X1, ,,Xn be iid with E(X1) = u and Var(X1) limiting distribution of nlog (1 +). o2. Find the where T n(X - 4)/s. - 1 - 4.(120) Let X1,,,Xn be iid r(, 1) and g(u)...
Let Xi,... ,Xn be i.i.d with pdf θνθ θ+1 where I(.) denotes the indicator function. (a) Find a 2-dimensional sufficient statistic for the mode (b) Suppose θ is a known constant. Find the MLE for v. (d) Suppose v-1. Find the MLE for and determine its asymptotic distribution. Carefully justify your answer and state any theorems that you use. (e) Suppose1. Find the asymptotic distribution of the MLE estimator of exp[- Let Xi,... ,Xn be i.i.d with pdf θνθ θ+1...
Let X1 , . . . , xn be n iid. random variables with distribution N (θ, θ) for some unknown θ > 0. In the last homework, you have computed the maximum likelihood estimator θ for θ in terms of the sample averages of the linear and quadratic means, i.e. Xn and X,and applied the CLT and delta method to find its asymptotic variance. In this problem, you will compute the asymptotic variance of θ via the Fisher Information....
Delta Theorem's application to MLES Suppose X1, X2, ... are iid Poi(). a. Find the MLE of h() = P(X = 0) b. Find its asymptotic distribution
Let Xi , X2,. … X, denote a random sample of size n > 1 from a distribution with pdf f(x:0)--x'e®, x > 0 and θ > 0. a. Find the MLE for 0 b. Is the MLE unbiased? Show your steps. c. Find a complete sufficient statistic for 0. d. Find the UMVUE for θ. Make sure you indicate how you know it is the UMVUE. Let Xi , X2,. … X, denote a random sample of size n...
8(100) Let X1,,Xn be iid from r(a, 6). (1)(50) Find the limiting distribution of the MLE of B. (2)(30) Find the limiting distribution of the MLE of B when a is known. (3)(20) Compare two asymptotic variances in (1) and (2), and make comment on it. 1ラ 8(100) Let X1,,Xn be iid from r(a, 6). (1)(50) Find the limiting distribution of the MLE of B. (2)(30) Find the limiting distribution of the MLE of B when a is known. (3)(20)...
use the delta method theorem to obtain the asymptotic distribution of R 39. The California (CA) Department of Conservation assigns a "CA Redemption Value' (CRV) to recycled material which is due some reimbursement. The "commingled rate R is defined as the following ratio for the population of recycled material of any given type: R weight of CRV material / total weight. The sampling distribution of R is not easy to obtain. Consider the following approach. Let p the proportion of...
253 42. Suppose that Xn B(n, p), and let p X/n. The CLT implies that se the 8-method theorem to identify the asymptotic distribution of the log odss g(β) = ln (p/0-p)) as n → 00,