Name: ________________________________________
22S:166 Computing in Statistics
Instructor: Cowles
PRACTICE PROBLEMS for Midterm 2, 2007
Instructions: You may use Windows R, or if you prefer, you may log into a Linux
computer and run Linux R. Copy and paste your solutions into this Word document.
Submit your exam by uploading the Word document into ICON.
1. The .75 quantile of a vector of sample values may be used to estimate the
population .75 quantile of the variable of interest.
a. Write an R function to get jackknife estimates of bias and standard error of this
estimator.
Copy your R code here.
b. Generate a vector of 20 random values from a Gamma distribution with
parameters 15 and 0.5. Use this vector as input to your function in part a.
Copy the R output here.
2. Is the jackknife “unbiased” estimate of the 0.75 quantile of a population
distribution really unbiased? Carry out a simulation study to find out for the case
when the sample size is 20 and the population distribution is Gamma(15, 0.5).
Note: when testing and debugging your code, use a very small number of
replicate datasets to save time. Using the jackknife within a simulation study is
time consuming, so you may do your final run with only 1000 replicate datasets.
Copy your R code here.
Copy your R output here.
Write a sentence or two interpreting your results here.
3. Note that the following R code may be used to produce a 90% bootstrap
percentile confidence interval for the .1 quantile of a population distribution based
on a single sample drawn from the population. In the example below, the data is
in a vector called “mydat.”
qfunc <- function(x, index) {quantile(x[index] , 0.1) }
