Questions & Answers

Comparison Of Estimators

tsakanikasnickos on Thursday, October 23 2014, 09:54 PM
0

Let  \( \displaystyle X_{1} , \dots , X_{n} \)  be a random sample from a population with probability density function  \( \displaystyle f(x ;\mu) = {e}^{ - (x-\mu)} \, , \, x \geq \mu \).  Which of the statistics



\[ \displaystyle T_{1}(X_{1} , \dots , X_{n}) = \min_{1\leq i\leq n } X_{i} - \frac{1}{n} \]

\[ \displaystyle T_{2}(X_{1} , \dots , X_{n}) = \frac{\sum_{i=1}^{n} X_{i} }{n} - 1 \]

is a better estimator than the other, if our loss function is the squared-error loss function?

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