Statistics Estimator Consistency

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In summary, the conversation discusses the consistency of two estimators, Ө1 and Ө2, for the interval (Ө, Ө+1). It is shown that Ө1=Ῡ -.5 and Ө2=Yn – (n/(n+1)) are both consistent estimators of Ө. The second part of the conversation involves discussing a power family distribution and its corresponding distribution function, Fn(y). It is then stated that Yn=max(Y1, Y2, …, Yn ) is a consistent estimator of Ө for this distribution.
  • #1
jmlink
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1) Distribution is a uniform distribution on the interval (Ө, Ө+1)
Show that Ө1 is a consistent estimator of Ө. Ө1=Ῡ -.5
Show that Ө2 is a consistent estimator of Ө. Ө2=Yn – (n/(n+1)).

2) I think the distribution for this one is a uniform distribution on the interval (0, Ө) but I am not 100% sure.
Let Y1, Y2, …, Yn denote a random sample of size n from a power family distribution. Then the method in Section 6.7 imply that Yn=max(Y1, Y2, …, Yn ) has the distribution function of:
0, y<0
Fn(y)= (y/ Ө)^(αn) , 0 ≤ y ≤ Ө
1, y> Ө

Show that Yn is a consistent estimator of Ө.
 
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  • #2
For 1 and 2 you need to state the distribution being sampled.
 

FAQ: Statistics Estimator Consistency

What is a statistics estimator consistency?

Statistics estimator consistency refers to the property of an estimator to produce results that are close to the true value of the population parameter as the sample size increases. In other words, the estimator becomes more accurate and reliable as more data is collected.

Why is statistics estimator consistency important in research?

Statistics estimator consistency is important because it ensures that the conclusions drawn from a study are based on accurate and reliable data. Without consistency, the results may be biased or misleading, leading to incorrect conclusions and decisions.

What are the factors that affect statistics estimator consistency?

The factors that can affect statistics estimator consistency include the sample size, the sampling method, and the assumptions made about the data. A larger sample size typically leads to better consistency, while biased sampling or incorrect assumptions can lead to inconsistency.

How is statistics estimator consistency measured?

Statistics estimator consistency is commonly measured using the mean squared error (MSE) or the mean absolute error (MAE). These metrics compare the estimated values to the true values and provide a measure of how close the estimator is to the true value.

Can an estimator be consistent in some cases but not in others?

Yes, an estimator can be consistent in some cases but not in others. This is known as asymptotic consistency, where the estimator becomes consistent only as the sample size approaches infinity. In some cases, the estimator may be consistent for certain population parameters but not for others.

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