Sufficient Statistics Homework Statement and Solution

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SUMMARY

The discussion centers on a homework problem related to sufficient statistics, specifically involving the estimation of an unknown mean from an exponentially distributed variable. The key insight is that the indicator function I(.) signifies that sampling values less than or equal to the mean μ is impossible, allowing for a focus solely on samples greater than μ. This simplification is crucial for deriving properties of the usual estimator in the context of frequentist statistics.

PREREQUISITES
  • Understanding of sufficient statistics in statistics
  • Familiarity with exponential distributions
  • Knowledge of frequentist estimation methods
  • Basic comprehension of indicator functions
NEXT STEPS
  • Study the properties of sufficient statistics in detail
  • Learn about the exponential distribution and its applications
  • Explore frequentist estimation techniques and their implications
  • Investigate the role of indicator functions in statistical modeling
USEFUL FOR

Students and professionals in statistics, particularly those focusing on estimation theory and sufficient statistics, will benefit from this discussion.

abeliando
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Homework Statement


Problem is in the attachment, sorry, I can't figure out how to do tex in this message board system.


Homework Equations





The Attempt at a Solution


In the attachment.
 

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I think you're into too much math. The I(.) function, if I get its meaning correctly, is nothing but to indicate that it is impossible to sample x\leq\mu. With frequentists' approach, this means a lot: you can safely ignore the bunch of I(.)'s and consider only those samples greater than \mu. This should solve the problem :wink:
 
abeliando said:

Homework Statement


Problem is in the attachment, sorry, I can't figure out how to do tex in this message board system.


Homework Equations





The Attempt at a Solution


In the attachment.

Ignoring the fancy notation, what you have for given, fixed μ is that Y = X-μ is exponentially distributed with unknown mean, and you are trying to estimate that mean. You are being asked to show some property of the "usual" estimate.
 

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