Determining which estimator to use (stats)

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SUMMARY

This discussion focuses on selecting an appropriate estimator for the parameter θ in a uniform distribution defined on the interval 0 ≤ X ≤ θ. Two estimators are presented: θ1 = (2/n) Ʃ Yi, which is derived from the method of moments, and θ2 = (n/θ)(y/θ)^(n-1), which is based on the maximum likelihood estimation (MLE) approach. Participants emphasize the importance of statistical properties in choosing between these estimators, particularly in the context of their application in class exercises.

PREREQUISITES
  • Understanding of uniform distribution and its probability density function (PDF).
  • Familiarity with method of moments estimator.
  • Knowledge of maximum likelihood estimation (MLE) techniques.
  • Basic statistical properties relevant to estimator selection.
NEXT STEPS
  • Study the derivation process for maximum likelihood estimators in uniform distributions.
  • Learn about the statistical properties of estimators, including bias and consistency.
  • Explore the method of moments in greater detail, including its applications and limitations.
  • Investigate real-world applications of uniform distribution estimators in statistical modeling.
USEFUL FOR

Statisticians, data analysts, and students studying statistical estimation techniques, particularly those focusing on uniform distributions and the comparison of different estimation methods.

jasper90
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Consider a uniform distribution on the interval 0≤ X ≤ θ. We are interested in estimated θ from a random sample of draws for the PDF. Two potential estimators are:

θ1 = (2/n) Ʃ Yi

and

θ2 = (n/θ)(y/θ)^(n-1)

which estimator would you prefer and why? What statistical properties did you use to decide?

Uniform distribution f(x)= 1/(B-A) for alpha < X < Beta

We use method of moments estimator and max likelihood estimator
 
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anyone?
 
jasper90 said:
anyone?

Sure. Show us what you have done so far. Those are the Forum rules, and are also the means of mastering the material and passing the course.

RGV
 
I really don't know. Every problem we have done in class was done the reverse way.

Like, I know for max likelihood estimator, we take the Ln of f(x) and then derive it. Then we set to 0 and solve for our estimator. But I have never had to choose one. I tried reversing the process, but it is definitely wrong.

I know I would be replacing B with θ1 and θ2.
 

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