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Ben
Ben
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Confidence Intervalinterval for a Uniform Distribution based on Method of Momentsparameter in uniform distribution using MOM estimator

Let $X_1,..,X_n$$X_1,..,X_n \sim \text{IID U}[\theta,\theta+1]$ be a random sample offrom a uniform distribution with the stipulated bounds depending on the parameter $X$~$U[\theta,\theta+1]$$\theta$. Given a sample of $n=100$ observations from that distribution, the following statistic was calculated:

$\sum\limits_{i=1}^n X_i = 350.492$$$\sum_{i=1}^n x_i = 350.492.$$

I need to calculate 90% asymptotic confidence interval for the unknown parameter $\theta$ by using the method of moments.

By the method of moments I have obtained that $\hat{\theta}_{mm} = \bar{X_n}-1/2$$\hat{\theta}_\text{MOM} = \bar{X_n}-1/2$. However, I am not sure how to proceed from here. Do I need to show that the obtained estimator is asymptotically normal and how can I find the asymptotic confidence interval?

Confidence Interval for a Uniform Distribution based on Method of Moments

Let $X_1,..,X_n$ be a random sample of $X$~$U[\theta,\theta+1]$. Given a sample $n=100$ from that distribution, the following statistic was calculated:

$\sum\limits_{i=1}^n X_i = 350.492$

I need to calculate 90% asymptotic confidence interval for the unknown parameter $\theta$ by using the method of moments.

By the method of moments I have obtained that $\hat{\theta}_{mm} = \bar{X_n}-1/2$. However, I am not sure how to proceed from here. Do I need to show that the obtained estimator is asymptotically normal and how can I find the asymptotic confidence interval?

Confidence interval for parameter in uniform distribution using MOM estimator

Let $X_1,..,X_n \sim \text{IID U}[\theta,\theta+1]$ be a random sample from a uniform distribution with the stipulated bounds depending on the parameter $\theta$. Given a sample of $n=100$ observations from that distribution, the following statistic was calculated:

$$\sum_{i=1}^n x_i = 350.492.$$

I need to calculate 90% asymptotic confidence interval for the unknown parameter $\theta$ by using the method of moments.

By the method of moments I have obtained that $\hat{\theta}_\text{MOM} = \bar{X_n}-1/2$. However, I am not sure how to proceed from here. Do I need to show that the obtained estimator is asymptotically normal and how can I find the asymptotic confidence interval?

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eliott
eliott
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Confidence Interval for a Uniform Distribution based on Method of Moments

Let $X_1,..,X_n$ be a random sample of $X$~$U[\theta,\theta+1]$. Given a sample $n=100$ from that distribution, the following statistic was calculated:

$\sum\limits_{i=1}^n X_i = 350.492$

I need to calculate 90% asymptotic confidence interval for the unknown parameter $\theta$ by using the method of moments.

By the method of moments I have obtained that $\hat{\theta}_{mm} = \bar{X_n}-1/2$. However, I am not sure how to proceed from here. Do I need to show that the obtained estimator is asymptotically normal and how can I find the asymptotic confidence interval?