Suppose we have three sets of random variables Wh, Xi, and Yj (for h= 1,...,k, i=...

70.2K

Verified Solution

Question

Statistics

Suppose we have three sets of random variables Wh, Xi, and Yj(for h= 1,...,k, i= 1,...,m, and j= 1,...,n) all of which aremutually independent. Assume that the three sets of randomvariables are all normally distributed with different means but thesame standard deviation. The MLE for the means are just the groupmeans and the MLE for the variance is the mean of the squarederrors of the observations from the groups when taking into accountthe group means. Write a function to fit the this model to threeobserved data vectors w, x, y and return both the MLE andlog-likelihood evaluated at the MLE. Use the commands
data("iris")
w = iris$Sepal.Width[iris$Sepecies=="setosa"]
x = iris$Sepal.Width[iris$Sepecies=="versicolor"]
y = iris$Sepal.Width[iris$Sepecies=="virginica"]
to make some data to analyze using your function. Compare theresults from analyzing the data with the model for difference meansto the results from analyzing the data when it would be assumedthat the means are all the same. Comment on your results.

Answer & Explanation Solved by verified expert

3.6 Ratings (547 Votes)

A statistic is a property of a sample whereas a parameter is a property of a population Often its natural to estimate a parameter such as the population mean by the corresponding property of the sample here the sample mean X Note that may be a vector or more complicated object Unobserved quantities are treated mathematically as random variables Potentially observable quantities are usually denoted by capital letters Xi X Y etc Once the data have been observed the values taken by these random See Answer

Get Answers to Unlimited Questions

Join us to gain access to millions of questions and expert answers. Enjoy exclusive benefits tailored just for you!

Membership Benefits:

Unlimited Question Access with detailed Answers
Zin AI - 3 Million Words
10 Dall-E 3 Images
20 Plot Generations
Conversation with Dialogue Memory
No Ads, Ever!
Access to Our Best AI Platform: Flex AI - Your personal assistant for all your inquiries!

Become a Member