Statistics- unbiased estimator

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In summary, an unbiased estimator in statistics is a method used to estimate population parameters that produces estimates that are on average equal to the true value. They are important because they provide accurate estimates and are essential for making reliable inferences. To determine if an estimator is unbiased, its average estimates can be compared to the true value or its expected value can be calculated. Examples of unbiased estimators include the sample mean, sample variance, and sample proportion. However, an unbiased estimator can still have a large amount of variability, which can be reduced by increasing the sample size.
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Homework Statement


A random sample of size 2, Y1 and Y2, is drawn from the pdf

fY(y;[tex]\vartheta[/tex])=2y*[tex]\vartheta[/tex]2, 0<y< 1/ [tex]\vartheta[/tex]

What must c equal if the statistic c(Y1+2Y2) is to be an unbiased estimator for 1 / [tex]\vartheta[/tex]

Homework Equations





The Attempt at a Solution



I tried to find the E[c(Y1+2Y2)] but don't really know how to reach 1 / [tex]\vartheta[/tex]

There is also the equation of the Ymax

maybe I should set them equal ? but how to get rid of Y1 and Y2 ?

Thanks.
 
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oh, I got it :\
 

What is an unbiased estimator in statistics?

An unbiased estimator in statistics is a method used to estimate a population parameter that, on average, produces an estimate that is equal to the true value of the parameter. This means that the estimator does not consistently overestimate or underestimate the true value, but rather provides an unbiased estimate that is close to the true value.

What is the importance of unbiased estimators in statistics?

Unbiased estimators are important in statistics because they provide accurate estimates of population parameters. This allows researchers to make more informed decisions and draw more reliable conclusions based on their data. Additionally, unbiased estimators are essential for making valid statistical inferences about a population.

How do you determine if an estimator is unbiased?

To determine if an estimator is unbiased, you can compare the average of its estimates to the true value of the population parameter. If the average estimate is equal to the true value, then the estimator is unbiased. This can also be mathematically proven by calculating the expected value of the estimator and comparing it to the true value.

What are some examples of unbiased estimators?

Some examples of unbiased estimators include the sample mean, sample variance, and sample proportion. These estimators are commonly used in statistics to estimate the population mean, variance, and proportion, respectively.

Can an unbiased estimator have a large amount of variability?

Yes, an unbiased estimator can have a large amount of variability. The unbiasedness of an estimator refers to its accuracy in estimating the true value, but it does not guarantee that the estimate will be precise or have low variability. In some cases, unbiased estimators may have a significant amount of variability, which can be reduced by increasing the sample size.

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