Determining which estimator to use (stats)

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In summary, we discussed two potential estimators for estimating θ in a uniform distribution on the interval 0≤ X ≤ θ. These estimators are θ1 = (2/n) Ʃ Yi and θ2 = (n/θ)(y/θ)^(n-1). To decide which estimator to prefer, we used the method of moments estimator and the maximum likelihood estimator. The method of moments estimator involves setting the sample moments equal to the theoretical moments and solving for the estimator, while the maximum likelihood estimator involves taking the natural log of the probability density function, setting it equal to 0, and solving for the estimator. Based on these properties, we would prefer the estimator that yields the most accurate
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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?
 
  • #3
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
 
  • #4
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.
 

1. What factors should be considered when choosing an estimator?

When determining which estimator to use in statistics, several factors should be considered. These include the type of data (continuous, discrete, categorical), sample size, distribution of the data, and the research question being investigated.

2. What is the difference between a parametric and non-parametric estimator?

A parametric estimator assumes that the data follows a specific distribution (e.g. normal distribution) and makes use of parameters to estimate population parameters. On the other hand, a non-parametric estimator does not make any assumptions about the underlying distribution of the data and instead uses ranks or medians to estimate population parameters.

3. How can I determine if my data follows a specific distribution?

There are several methods to determine the distribution of your data, such as visual inspection of a histogram or a Q-Q plot, conducting a goodness-of-fit test, or using statistical software to fit different distributions and compare their goodness-of-fit measures.

4. Can I use the same estimator for different research questions?

The choice of estimator should be based on the research question and the type of data being investigated. While some estimators may be suitable for multiple research questions and data types, it is important to carefully consider the assumptions and limitations of each estimator before using it for a different research question.

5. How do I know if my chosen estimator is providing accurate results?

One way to assess the accuracy of an estimator is to use simulation studies where the true values of the population parameters are known and can be compared to the estimates provided by the estimator. Additionally, conducting sensitivity analyses by varying assumptions and parameters can also help determine the robustness of the estimator.

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