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iid Consider data X1, X2, . .. , Xn Ber(0). Consider the following two estimators of 0 Ô1 = X, and Ô2 1+E, X; i=1 2+ n 1. Compute the Bias of both 6, and Ô2. Which estimator has lower bias? 2. Compute the variance of 0, and 02. Which estimator has lower variance? Hint: com- pute the ratio of Var[01]/Var[02] and see if the ratio is less than, equal to, or greater than 1. 3. Compute the MSE of 01 and 02 using the results of the previous parts. One way of showing an estimator is consistent is by showing that the MSE –→ 0 as n → xo. Are 01 and 02 consistent?

iid Consider data X1, X2, . .. , Xn Ber(0). Consider the following two estimators of 0 Ô1 = X, and Ô2 1+E, X; i=1 2+ n 1. Compute the Bias of both 6, and Ô2. Which estimator has lower bias? 2. Compute the variance of 0, and 02. Which estimator has lower variance? Hint: com- pute the ratio of Var[01]/Var[02] and see if the ratio is less than, equal to, or greater than 1. 3. Compute the MSE of 01 and 02 using the results of the previous parts. One way of showing an estimator is consistent is by showing that the MSE –→ 0 as n → xo. Are 01 and 02 consistent?

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Consider data X1, X2, ... , Xn iid Ber(0). Consider the following two estimators of 0 1+E X; Ô, = X, and Ô2 2+ n 1. Compute the Bias of both 6, and 02. Which estimator has lower bias? 2. Compute the variance of 01 and 02. Which estimator has lower variance? Hint: com- pute the ratio of Var(01]/Var[02] and see if the ratio is less than, equal to, or greater than 1. 3. Compute the MSE of 01 and 02 using the results of the previous parts. One way of showing an estimator is consistent is by showing that the MSE → 0 as n → xo. Are 0, and 02 consistent?
Transcribed Image Text:Consider data X1, X2, ... , Xn iid Ber(0). Consider the following two estimators of 0 1+E X; Ô, = X, and Ô2 2+ n 1. Compute the Bias of both 6, and 02. Which estimator has lower bias? 2. Compute the variance of 01 and 02. Which estimator has lower variance? Hint: com- pute the ratio of Var(01]/Var[02] and see if the ratio is less than, equal to, or greater than 1. 3. Compute the MSE of 01 and 02 using the results of the previous parts. One way of showing an estimator is consistent is by showing that the MSE → 0 as n → xo. Are 0, and 02 consistent?
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