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Question

Math 6010 • Linear Models

Spring 2020 • Question 8

Question

Math 6010 • Linear Models Spring 2020 • Question 8

Let \(X_1,\ldots ,X_n\sim N(\mu _1,1)\) and \(Y_1,\ldots ,Y_m\sim N(\mu _2,1)\), where all random variables are independent. Derive the likelihood ratio test for \[ H_0:\mu _1^2=\mu _2^2 \quad \text {vs.}H_a:\mu _1^2\ne \mu _2^2. \] What is the distribution of the test statistic?

Raw LaTeX

Let \(X_1,\ldots,X_n\sim \N(\mu_1,1)\) and
\(Y_1,\ldots,Y_m\sim \N(\mu_2,1)\), where all random variables are independent.
Derive the likelihood ratio test for
\[
  H_0:\mu_1^2=\mu_2^2 \quad \text{vs.}H_a:\mu_1^2\ne\mu_2^2.
\]
What is the distribution of the test statistic?

Topic Tags

Covariance and Independence F-Tests and t-Tests Likelihood Ratio Tests Maximum Likelihood Estimation