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i.i.d. Suppose X1,..., X, Uniform[0, 0] with unknown 0. Consider the following three estima- tors for 0: 0 = max X1,..., X, n + 1 max X1, ..., X, n n+2 max X1,..., X n+1 Use the R code "Week 4 - compare estimators for uniform.R" in Canvas/Files/Discussion to conduct simulations to compare the three estimators in terms of their bias, standard error (SE), and mean squared error (MSE). In the simulation, suppose the true 0 = 1. (a each of the three estimators from the simulation. Present your simulation result in the Simulate 10000 data sets with n = 10. Compute the bias, SE and MSE of

i.i.d. Suppose X1,..., X, Uniform[0, 0] with unknown 0. Consider the following three estima- tors for 0: 0 = max X1,..., X, n + 1 max X1, ..., X, n n+2 max X1,..., X n+1 Use the R code "Week 4 - compare estimators for uniform.R" in Canvas/Files/Discussion to conduct simulations to compare the three estimators in terms of their bias, standard error (SE), and mean squared error (MSE). In the simulation, suppose the true 0 = 1. (a each of the three estimators from the simulation. Present your simulation result in the Simulate 10000 data sets with n = 10. Compute the bias, SE and MSE of

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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i.i.d. Suppose X1,..., X, ' Uniform[0, 6] with unknown 0. Consider the following three estima- tors for 0: = max X,..., X, n + 1 max X1, .. Xm n n + 2 max X1, ... , Xn n + 1 Use the R code "Week 4 - compare estimators for uniform.R" in Canvas/Files/Discussion to conduct simulations to compare the three estimators in terms of their bias, standard error (SE), and mean squared error (MSE). In the simulation, suppose the true 0 = 1. (a, Simulate 10000 data sets with n = 10. Compute the bias, SE and MSE of each of the three estimators from the simulation. Present your simulation result in the following table. Then answer: Which one has the smallest bias? Which one has the smallest SE? Which one has the smallest MSE? 3 bias SE MSE 02 Table 1: Performance measure with n = 10 (b) pute the bias, SE and MSE of each of the three estimators from the simulation. Present Simulate 10000 data sets for each of the following n: n = 10, 20, 50, 100. Com- your simulation result in the following table. Then answer: Do you observe any pattern for each of the performance measures (bias, SE, MSE) as n increases? Do the three estimators perform more similarly as n gets larger? Can you provide some intuitive explanation for this? bias SE MSE 02 n = 10 n = 20 n = 50 n = 100 Table 2: Performance measure with n = 10, 20, 50, 100
Transcribed Image Text:i.i.d. Suppose X1,..., X, ' Uniform[0, 6] with unknown 0. Consider the following three estima- tors for 0: = max X,..., X, n + 1 max X1, .. Xm n n + 2 max X1, ... , Xn n + 1 Use the R code "Week 4 - compare estimators for uniform.R" in Canvas/Files/Discussion to conduct simulations to compare the three estimators in terms of their bias, standard error (SE), and mean squared error (MSE). In the simulation, suppose the true 0 = 1. (a, Simulate 10000 data sets with n = 10. Compute the bias, SE and MSE of each of the three estimators from the simulation. Present your simulation result in the following table. Then answer: Which one has the smallest bias? Which one has the smallest SE? Which one has the smallest MSE? 3 bias SE MSE 02 Table 1: Performance measure with n = 10 (b) pute the bias, SE and MSE of each of the three estimators from the simulation. Present Simulate 10000 data sets for each of the following n: n = 10, 20, 50, 100. Com- your simulation result in the following table. Then answer: Do you observe any pattern for each of the performance measures (bias, SE, MSE) as n increases? Do the three estimators perform more similarly as n gets larger? Can you provide some intuitive explanation for this? bias SE MSE 02 n = 10 n = 20 n = 50 n = 100 Table 2: Performance measure with n = 10, 20, 50, 100
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