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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6010 • Linear Models

Spring 2016 • Question 4

Question

Math 6010 • Linear Models Spring 2016 • Question 4

Assume that \(X_1,\ldots ,X_n\) are a random sample with common pdf \(f(x;\theta )=(\theta +1)x^{-\theta -2}\) for \(x>1\), and zero otherwise. Is the method of moments estimator for \(\theta \) the same as the maximum likelihood estimator for \(\theta \)?

Raw LaTeX

Assume that \(X_1,\ldots,X_n\) are a random sample with common pdf
\(f(x;\theta)=(\theta+1)x^{-\theta-2}\) for \(x>1\), and zero otherwise. Is the
method of moments estimator for \(\theta\) the same as the maximum likelihood
estimator for \(\theta\)?

Topic Tags

Estimator Distributions Likelihood Ratio Tests Maximum Likelihood Estimation Uniform Integrability and Truncation Methods