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consider a ratio estimator
1. Consider a ratio estimator h(01,02) 1/02, where the estimated variance- Го, is covariance for ô...
consider a ratio estimator by using delta method 1. Consider a ratio estimator h(1,6%) = 61/62, where the estimated variance- covariance for = | û lên] Covlên, ô2) vCov(@) = Covlê, ê2) Û @2]] Using the delta method, show that VẪhê, 2) = [1/8, -6,163 Cov(6) [ B.
Exercise 2b please! Exercise 1 Consider the regression model through the origin y.-β1zi-ci, where Ei ~ N(0,o). It is assumed that the regression line passes through the origin (0, 0) that for this model a: T N, is an unbiased estimator of o2. a. Show d. Show that (n-D2 ~X2-1, where se is the unbiased estimator of σ2 from question (a). Exercise2 Refer to exercise 1 a. Show that is BLUE (best linear unbiased estimator) b. Show that +1 has...
1. A simple regression model is given by Y81B2X+ e for t 1, (1) ,n errors e with Var (e) a follow AR(1) model where the regression et pet-1 + , t=1...n where 's are uncorrelated random variables with constant variance, that is, E()0, Var (v) = , Cov (, ,) 0 for t Now given that Var (e) = Var (e1-1)= , and Cov (e-1, v)0 (a) Show that (b) Show that E (ee-1)= p. (c) What problem(s) will...
(3) Suppose that E (0,) θ, Ε(92) θ,V(91) of, and V(02) σ . Assume that 0, and θ2 are independent. Consider the following estimator: 6, - a+(1 -@ (a) Show that @g is unbiased for θ (b) Find the value of a that minimizes the variance of 03 (c) Which estimator would you use? θί,02, or th when using the value of a found in part (b)
id 3. Let X1, X2, ..., X 1 N(0,03) and Y1, 72,..., Ym N(02,03) independently. Denote 0 = (01,02,0z)" (a) Write down the expression for the log-likelihood function (0). (b) Find the maximum likelihood estimator Ô of . (You do not need to perform the second derivative test.) (e) Find the Fisher information. (d) Consider using –2 log(LR) to test H. : 0 = 0against H, : 01 + 02. Find the maximum likelihood estimator of O under H, and...
arccoth Cz)- 1/2 ln (z+1)/(z-1)) Screenshot 2019-01-17 at 20.14.00 CSC (x) 6 Consider taking a simple random sample (SRS) of size 2 from the population and assume further that E(r2)Xwhere Xis the population mean. (0) Show that the estimato is an unbiased estimator of X XN with population variance S2. Suppose that r1 and r2 are obtained (1 mark) (5 marks,) (4 marks) (-x)tan Cx) (i) Show that cov(1,2) i) Using the result from(ii) show that var ()1- (iv) Using...
1. (40) Suppose that X1, X2, .. , Xn, forms an normal distribution with mean /u and variance o2, both unknown: independent and identically distributed sample from 2. 1 f(ru,02) x < 00, -00 < u < 00, o20 - 00 27TO2 (a) Derive the sample variance, S2, for this random sample (b) Derive the maximum likelihood estimator (MLE) of u and o2, denoted fi and o2, respectively (c) Find the MLE of 2 (d) Derive the method of moment...
QUESTION4 (a) Let e be a zero-mean, unit-variance white noise process. Consider a process that begins at time t = 0 and is defined recursively as follows. Let Y0 = ceo and Y1-CgY0-ei. Then let Y,-φ1Yt-it wt-1-et for t > ï as in an AR(2) process. Show that the process mean, E(Y.), is zero. (b) Suppose that (a is generated according to }.-10 e,-tet-+扣-1 with e,-N(0.) 0 Find the mean and covariance functions for (Y). Is (Y) stationary? Justify your...
Let X1,..., X, be a random sample from a Bernoulli(p) where p 1-(1-q*is the probability of a positive test when a test is conducted on a group of k subjects from a population with a prevalence rate of q. The estimated prevalence rate is l/k 9-1-(1-X) Using the Delta Method find the approximate variance of the estimator q.
Question 2 (10 points) You are given the following model y-put ei. Consider two alternative estimators of β, b2xvix? and b = Zy/X 1. Which estimator would you choose and why if the model satisfies all the assumptions of classical regression? Prove your results. (4 points) 2. Now suppose that var(y)-hxi, where h is a positive constant (a) Obtain the correct variance of the OLS estimator. (2 points) (b) Show that the BLU estimator is now 6. Derive its variance....