Monte Carlo Simulation and Confidence Intervals Homework, Assignments of Statistics

Download Monte Carlo Simulation and Confidence Intervals Homework and more Assignments Statistics in PDF only on Docsity! Homework 7B Assigned: 31 October 2008 Due: 17 November 2008 Exercises 1. Conduct a small Monte Carlo simulation to examine the behavior of t-based CIs for the mean of a Poisson distribution. Recall that a Poisson random variable can be used to model unbounded counts (0, 1, 2, 3, …). If Y ~ Poisson(μ), then E(Y) = V(Y) = μ. Compare two confidence interval procedures in terms of coverage and length: i) n s tY yn 1,2/1 −−± α ii) 2 1,2/1 ⎭ ⎬ ⎫ ⎩ ⎨ ⎧ ± −− n stX xnα where ii YX = Select at least 3 values of “mu” (say 2, 10, 25) and 3 values of “n” for this illustration (say n=15, 30, and 50). 2. Construct a 95% BCa (bias-corrected and accelerated) bootstrap CI for the mean “mpg” variable. [Do not do this for homework: it would be a candidate project for an interested student.] 3. Construct a 95% confidence interval for the variance of the “mpg” sample data given below. Use percentile-based bootstrap methods to obtain this interval. These data are from the “cars” data set found on http://lib.stat.cmu.edu. The description of these data can be found at the StatLib website. We consider the 1982 subset of a larger data set containing 406 observations on the following 8 variables: MPG (miles per gallon), # cylinders, engine displacement (cu. inches), horsepower, vehicle weight (lbs.), time to accelerate from O to 60 mph (sec.),model year (modulo 100), and origin of car (1. American, 2. European, 3. Japanese). Missing data values are denoted NA below. Variables: mpg / cylinders / displacement / horsepower / weight acceleration / model.year /origin 28.0 4. 112.0 88.00 2605. 19.6 82. 1. 27.0 4. 112.0 88.00 2640. 18.6 82. 1. 34.0 4. 112.0 88.00 2395. 18.0 82. 1. 31.0 4. 112.0 85.00 2575. 16.2 82. 1. 29.0 4. 135.0 84.00 2525. 16.0 82. 1. 27.0 4. 151.0 90.00 2735. 18.0 82. 1. 24.0 4. 140.0 92.00 2865. 16.4 82. 1. 23.0 4. 151.0 NA 3035. 20.5 82. 1. 36.0 4. 105.0 74.00 1980. 15.3 82. 2. 37.0 4. 91.00 68.00 2025. 18.2 82. 3.