Rules

See the Section about Rules for Quizzes and Homeworks on the General Info page.

Your work handed into Canvas should be an Rmarkdown file with text and code chunks that can be run to produce what you did. We do not take your word for what the output is. We may run it ourselves. But we also want the output.

You may ask questions during the quiz, especially if the wording of a question is confusing or there seems to be an issue with the question, but the instructor will not be giving hints.

You must be in the classroom, Molecular and Cellular Biology 2-120, to take the quiz.

Quizzes must uploaded by the end of class (1:10). It should actually allow a few minutes after that, but those not uploaded by 1:10 will be marked late. Here is the link for uploading this quiz https://canvas.umn.edu/courses/330843/assignments/2864737.

Quiz 5

Problem 1

The following R command 


foo <- read.table(url("https://www.stat.umn.edu/geyer/3701/data/2022/q5p1.txt"), header = TRUE)
assigns one R object foo, which is a dataframe containing one variable x.

We assume these data are independent and identically distributed from the logistic location family. See the help for R function dlogis for a description of this family. We assume the default value (1) for the scale parameter.

  1. Find the MLE for these data. Good starting points (root-n-consistent estimators) for this model include both the sample mean and the sample median (also any trimmed mean).
  2. Produce a large-sample approximate 95% confidence interval the true unknown location parameter from these data using the usual theory of asymptotics of maximum likelihood.

Problem 2

This problem continues where the preceding problem left off. We use the same data and the same statistical model.

Also produce a large-sample approximate 95% confidence interval for the parameter that is a level set of the log likelihood, following Section 5.4.4 of the course notes on models, part II.

Problem 3

The following R command 


load(url("https://www.stat.umn.edu/geyer/3701/data/2022/q5p3.rda"))
loads one R object f, which is a function having one argument, which is a four-dimensional numeric vector. The value of this function is numeric scalar.

The problem is to minimize this function.

This function has been deliberately constructed to have multiple local minima. So use R function optim with method = "SANN" to try to minimize it (Section 7.1.2.3 of the notes on optimization).

Since this method uses random search, use R function set.seed to get repeatability as you work on this problem.

Use R function optim method = "SANN" ten different times with default arguments of the control parameters starting at zero (in four-dimensional space). Do you always get the same answer? What does this tell you about method SANN?