consider a ratio estimator
by using delta method
consider a ratio estimator by using delta method 1. Consider a ratio estimator h(1,6%) = 61/62,...
1. Consider a ratio estimator h(01,02) 1/02, where the estimated variance- Го, is covariance for ô Cov(o,O2) Cov (0) ΙGov(0, 6.) Using the delta method, show that 1/0 V,6) [1/ -0,/0 vCov( -01/05
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....
Question 1. Consider a stratified design composed of H strata of size Nh, h = 1,...,H. We want to estimate the population mean µy of the characteristic y. Let µx,h, h =1,...,H be the means in the strata (in the population) of an auxiliary characteristic x. The µx,h are supposedly known and we propose to estimate µy using the following estimator: b µD = yst +µx −xst where yst and xst are the basic estimate of the population means µy...
Question 1 Consider the following model Yi = B.z; + u (a) Derive the OLS estimator of B, B. (6 marks] (b) Show that is unbiased. [9 marks] (c) Find the variance of B. [7 marks]
7.20 Consider Y1,...,Yn as defined in Exercise 7.19. (a) Show that Yilti is an unbiased estimator of B. (b) Calculate the exact variance of Yi/ xi and compare it to the variance of the MLE. 7.19 Suppose that the random variables Yı, ..., Yn satisfy Yi = Bli +ti, i = 1,...,n, where x1, ..., In are fixed constants, and €1,..., En are iid n(0,02), o2 unknown. (a) Find a two-dimensional sufficient statistic for (0,0%). (b) Find the MLE of...
EXERCISE1 The robust estimator of of the variogram (Cressie and Hawkins (1980)) given by 1 uses the transformation 2s+h)-Z(s 0.494 27(h) Consider now the class of power transformations Z(s + h) - Z(s) 27(h) 름, a. Find the mean and variance of a λwhere λ- b. b. Let X ~ χ. Find and plot the pdf of Y-X, where λ- c. Find an estimator of the variogram when the transformations , 2' 3' 5' 8 Z(s+ h) - Z(s) Z(s...
Question 1 Consider the following model Yi = Bx; +ui (a) Derive the OLS estimator of B, ß. (6 marks] (b) Show that B is unbiased. (9 marks] (c) Find the variance of ß. [7 marks] -r.pdf
Consider the following assumptions: 1. ?? = ?(? + ??) (data generating process) 2. E(?? ) = 0 for all 3. Var(?? ) = ? 2 for all i 4. Cov(?? , ?? ) for ? ≠ ? 5. ?? ∼ ?????? And suppose you’re interested in generating an estimate for ?. a. What is the expected value of the sample mean estimator, ?̂= 1 ? ∑?? , under these assumptions? Is ?̂an unbiased estimator for ?? Show all work...
2. Suppose Y1,...,Yn are IID discrete random variables with P(Y; = 0) = 60 P(Y; = 1) = 01, P(Y; = 2) = 62, where the parameter vector 6 = (60,61,62) satisfies: 0; > 0 and 200; = 1. (a) Calculate E[Y] and EY?), and use the results to derive a method of moments estimator for the parameters (01,02). (b) Show that the maximum likelihood estimator for 6 = 60, 61, 62) is - Ôno = ôz = = 1(Y;=0),...
6. Consider the following sample: Xi = -2, X2 = 12. X7-1.5, Xs -0.5, a. Estimate the population mean, μ, using an analogical estimator. b. Estimate the population variance. ơ2, using a biased and an unbiased estimator. c. Assuming that the random sample is drawn from a normal population with known variance, σ2-4, construct a 95% confidence interval for the population mean. d. Assuming that the random sample is drawn from a normal population with unknown variance, σ2, construct a...