hey I need solution asap
thank you
provide step by step solution please
que 5
(a) Find and-2 logA. (b) Determine the Wald-type test. (c) What is Rao's score statistic? 5. Let ...
Let X1, ,Xn be a random sample gamma(α, β), assume a is known. Consider testing Ho : β = βο. Derive Wald statistic for testing Ho using the MLE of B both in the numerator and denominator of the statistic.
Let X1, ,Xn be a random sample gamma(α, β), assume a is known. Consider testing Ho : β = βο. Derive Wald statistic for testing Ho using the MLE of B both in the numerator and denominator of the statistic.
1. Let X1, ..., Xn be iid with PDF 1 xle f(x;0) = x>0 (a) Determine the likelihood ratio test to test Ho: 0 = 0, versus H:0700 (b) Determine Wald-type test to test Ho: 0 = 0, versus Hį:0 700 (C) Determine Rao's score statistic to test Ho: 0 = 0, versus Hų:0 700
2. Let Xi, , Х, be a random sample gamma(a, β). In parts (a-(d) assume a is known. 30 points a. Consider testing H. : β--βο. Derive Wald statistic for testing H, using the MLE of B both in the numerator and denominator of the statistic. b. Derive a test statistic for testing H, using the asymptotic distribution of the MLE of β. What is the relation between the two statistics in parts (a) and (b)? c. Derive the Score...
Let X1, , Xn be a random sample gamma(α, β), assume a is known. Consider testing Ho : β-A-Derive the Score test for testing Ho-
Let X1, , Xn be a random sample gamma(α, β), assume a is known. Consider testing Ho : β-A-Derive the Score test for testing Ho-
, Xn iid. N 5. Let Xi, (μ, σ2), μ E R and σ2 > 0 are both unknown. Find an asymp- totically likelihood ratio test (LRT) of approximate size α for testing μ-σ 2 H1:ťtơ2 Ho : versus
, Xn iid. N 5. Let Xi, (μ, σ2), μ E R and σ2 > 0 are both unknown. Find an asymp- totically likelihood ratio test (LRT) of approximate size α for testing μ-σ 2 H1:ťtơ2 Ho : versus
Consider a random sample X1, ..., Xn from a normal distribution with known mean 0 and unknown variance 0 = 02 (a) Write the likelihood and log-likelihood function (b) Derive the maximum likelihood estimator for 6 (c) Show that the Fisher information matrix is I(O) = 2014 (d) What is the variance of the maximum likelihood estimator for @? Does it attain the Cramer-Rao lower bound? (e) Suppose that you are testing 0 = 1 versus the alternative 0 #...
3. Let Ya» . . . , Yn be independent normally distributed random variables with E(X) Gai and V(X)-1. Recall that the normal density with mean μ and variance σ given by TO 202 (a) Find the maximum likelihood estimator β of β (b) Show that ß is unbiased. (c) Determine the distribution of β (d) Recall that the likelihood ratio test of Ho : θ 02] L1] L2] θ° is to θ0 against H1: θ reject Ho if L(e)...
2. (a) Suppose that x1,... , Vn are a random sample from a gamma distribution with shape parameter α and rate parameter λ, Here α > 0 and λ > 0. Let θ-(α, β). Determine the log-likelihood, 00), and a 2-dimensional sufficient statistic for the data (b) Suppose that xi, ,Xn are a random sample from a U(-9,0) distribution. f(x; 8) otherwise Here θ > 0, Determine the likelihood, L(0), and a one-dimensional sufficient statistic. Note that the likelihood should...
4. (20 pts) ( Problem 10.13, Wasserman) Let X 1, , xn v N4ơ2) where σ2 is known H +io. (a) (8 pts) Construct a level α Wald test and specify the rejection region. (You may use the a-quantile (b) (12 pts) Construct a level α likelihood ratio test and specify the rejection region. Compare the result 0:μ-μ0 versus H1 : μ za of standard normal.) with (a). (You may use the a-quantile X2,a ond distribution. )
1.(c)
2.(a),(b)
5. Let Xi,..., X, be iid N(e, 1). (a) Show that X is a complete sufficient statistic. (b) Show that the UMVUE of θ 2 is X2-1/n x"-'e-x/θ , x > 0.0 > 0 6. Let Xi, ,Xn be i.i.d. gamma(α,6) where α > l is known. ( f(x) Γ(α)θα (a) Show that Σ X, is complete and sufficient for θ (b) Find ElI/X] (c) Find the UMVUE of 1/0 -e λ , X > 0 2) (x...