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Department of Mathematics

Question

Math 6010 • Linear Models

Fall 2017 • Question 10

Question

Math 6010 • Linear Models Fall 2017 • Question 10

Let \(X_1,X_2,\ldots ,X_n\) be iid with common pdf \[ f(x;\theta )=\frac {\theta }{(1+x)^{\theta +1}}, \qquad 0<x<\infty ,\ \theta >0. \] What is a lower bound for the variance of an unbiased estimator of \(\theta \)?

Raw LaTeX

Let \(X_1,X_2,\ldots,X_n\) be iid with common pdf
\[
  f(x;\theta)=\frac{\theta}{(1+x)^{\theta+1}}, \qquad
  0<x<\infty,\ \theta>0.
\]
What is a lower bound for the variance of an unbiased estimator of \(\theta\)?

Topic Tags

Analysis of Variance Estimator Distributions Measure-Theoretic Probability Uniform Integrability and Truncation Methods