Biased and unbiased estimators

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In summary, the conversation discusses the use of biased and unbiased estimators in statistics. While biased estimators may not accurately reflect the population statistic being estimated, they may be the only option available due to practical reasons such as biased measurements from sensors. In these cases, the biased estimator can still be useful if the sensor model accounts for the bias. However, the preference is still for unbiased estimators whenever possible.
  • #1
thrillhouse86
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Hey All,

I am comfortable with the idea of biased and unbiased estimators, but what I don't understand is why you would ever want to use a biased estimator ? at the end of the day doesn't it mean that the sample statistic is different from the population statistic you are trying to estimate ?
 
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  • #2
thrillhouse86 said:
but what I don't understand is why you would ever want to use a biased estimator ?
The simple answer is that the biased estimator might be all you have available. Lots of sensors yield biased measurements. The sensor model had better include an estimation of the bias to yield an answer closer to the truth than that produced directly by the sensor.
 
  • #3
So does that mean you never really want a biased estimator, but sometimes practical issues force you to work with one ?
 
  • #5
cool thanks D H
 

1. What is the difference between biased and unbiased estimators?

Biased estimators are statistical tools that consistently overestimate or underestimate the true value of a population parameter, while unbiased estimators have no systematic tendency to over- or underestimate the parameter.

2. How can I identify if an estimator is biased or unbiased?

One way to identify if an estimator is biased is by comparing its expected value to the true value of the population parameter. If the expected value is equal to the true value, then the estimator is unbiased. If the expected value is consistently different from the true value, then the estimator is biased.

3. Can biased estimators still be useful?

Yes, biased estimators can still be useful in certain situations. For example, if the bias is small and the estimator has low variance, it may still be a better choice than an unbiased estimator with high variance. Additionally, some biased estimators can be corrected using statistical techniques.

4. What are the potential consequences of using a biased estimator?

Using a biased estimator can lead to incorrect conclusions and inferences about the population. It can also result in biased decision-making and inaccurate predictions. Additionally, biased estimators may not be as efficient as unbiased estimators, meaning they require a larger sample size to achieve the same level of accuracy.

5. How can we minimize bias in estimators?

One way to minimize bias in estimators is by using a larger sample size, as this can reduce the impact of random sampling error. Additionally, using more precise and accurate measurement tools can help reduce bias. Another approach is to use multiple estimators and compare their results to identify and correct any bias. Finally, understanding the underlying assumptions and limitations of the estimator can also help minimize bias.

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