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Suppose we have an estimator T for which the following two properties hold: The bias of T goes to zero as the sample size goes to infinity The variance of T goes to zero as the sample size goes to infinity Based on this information alone, what can we conclude about the estimator T

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hihirasohail

Answer:

We can make the following conclusions about T based on the given information:

  1. T is asymptomatically unbiased
  2. T is efficient relative to every other estimator
  3. T is consistent

Step-by-step explanation:

Such an estimator as described in the question statement possesses the property that as the amount of data points grow larger and larger towards an indefinite value, the estimates made as a result converge in probability to θ[tex]_{0}[/tex]. As more and more data is collected and added to the sample, the property of consistency is acquired.

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