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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6010 • Linear Models

Spring 2020 • Question 4

Question

Math 6010 • Linear Models Spring 2020 • Question 4

Let \(X_1,X_2,\ldots ,X_n\) be independent identically distributed random variables with density function \[ f(t\theta )=\frac {1}{2}e^{-|t-\theta |}, \qquad -\infty <t<\infty . \] The parameter \(\theta \) could be any real number. Find all maximum likelihood estimators for \(\theta \).

Raw LaTeX

Let \(X_1,X_2,\ldots,X_n\) be independent identically distributed
random variables with density function
\[
  f(t\theta)=\frac{1}{2}e^{-|t-\theta|}, \qquad -\infty<t<\infty.
\]
The parameter \(\theta\) could be any real number. Find all maximum likelihood
estimators for \(\theta\).

Topic Tags

Covariance and Independence Estimator Distributions Maximum Likelihood Estimation Uniform Integrability and Truncation Methods