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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6010 • Linear Models

2006 • Question 1

Question

Math 6010 • Linear Models 2006 • Question 1

Let \(X_1, X_2, \ldots \) be an i.i.d. sample from the uniform distribution on \([\theta , 1+\theta ]\), where \(\theta > 0\) is unknown. Is there an unique maximum likelihood estimator of \(\theta \) that is based on \(\{X_i\}_{i=1}^{\infty }\)? Prove or disprove.

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Let \(X_1, X_2, \ldots\) be an i.i.d. sample from the uniform distribution on \([\theta, 1+\theta]\), where \(\theta > 0\) is unknown. Is there an unique maximum likelihood estimator of \(\theta\) that is based on \(\{X_i\}_{i=1}^{\infty}\)? Prove or disprove.

Topic Tags

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