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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6010 • Linear Models

2006 • Question 2

Question

Math 6010 • Linear Models 2006 • Question 2

Suppose \(X_1, \ldots , X_n\) is an i.i.d. sample from the exponential density with mean \(\theta \), where \(\theta > 0\) is unknown. Find an estimator of \(\theta \) based on \(X_1, \ldots , X_n\). Is your estimator complete? Is it sufficient? Justify your reasoning.

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Suppose \(X_1, \ldots, X_n\) is an i.i.d. sample from the exponential density with mean \(\theta\), where \(\theta > 0\) is unknown. Find an estimator of \(\theta\) based on \(X_1, \ldots, X_n\). Is your estimator complete? Is it sufficient? Justify your reasoning.

Topic Tags

Estimator Distributions Exponential Martingales Measure-Theoretic Probability Uniform Integrability and Truncation Methods