Determining which estimator to use (stats)

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Homework Help Overview

The discussion revolves around estimating the parameter θ of a uniform distribution defined on the interval 0 ≤ X ≤ θ, using two proposed estimators derived from a random sample. Participants are exploring the statistical properties that might guide the choice between these estimators.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants are considering the method of moments and maximum likelihood estimators as potential approaches. There is a question regarding the preference for one estimator over the other and the statistical properties that could influence this decision.

Discussion Status

The discussion appears to be in an early stage, with some participants expressing uncertainty about the process of choosing between the estimators. One participant has requested others to share their progress, indicating a collaborative effort to clarify understanding.

Contextual Notes

One participant notes that previous class problems were approached differently, suggesting a potential gap in experience with this type of problem. There is also mention of reversing the typical process for deriving estimators, which raises questions about assumptions and methods being applied.

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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