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The statistic T is said to be a consistent estimator of the population parameter Q if
- a)E(T) = Q
- b)V(T) ⇒ o as n → ∞
- c)Both (A) and (B)
- d)None of the above
Correct answer is option 'C'. Can you explain this answer?
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The statistic T is said to be a consistent estimator of the population...
Consistent Estimator Explanation:
To determine whether a statistic T is a consistent estimator of the population parameter Q, we need to consider two main criteria:
Expectation of T:
- The first criteria is that the expected value of the estimator T should be equal to the population parameter Q. This is denoted by E(T) = Q. If the expected value of T converges to the true population parameter as the sample size approaches infinity, then T is said to be consistent.
Variance of T:
- The second criteria is that the variance of the estimator T should approach zero as the sample size grows larger. This is denoted by V(T) ⇒ 0 as n → ∞. A consistent estimator should have a variance that decreases as more data is collected.
Combination of Criteria:
- If both of these criteria are satisfied, then the statistic T is considered to be a consistent estimator of the population parameter Q. This means that as the sample size increases, the estimator T will provide more accurate estimates of the true population parameter.
Therefore, the correct answer is option 'C' which states that both the expectation of T being equal to Q and the variance of T approaching zero as the sample size increases are necessary conditions for T to be a consistent estimator.
To determine whether a statistic T is a consistent estimator of the population parameter Q, we need to consider two main criteria:
Expectation of T:
- The first criteria is that the expected value of the estimator T should be equal to the population parameter Q. This is denoted by E(T) = Q. If the expected value of T converges to the true population parameter as the sample size approaches infinity, then T is said to be consistent.
Variance of T:
- The second criteria is that the variance of the estimator T should approach zero as the sample size grows larger. This is denoted by V(T) ⇒ 0 as n → ∞. A consistent estimator should have a variance that decreases as more data is collected.
Combination of Criteria:
- If both of these criteria are satisfied, then the statistic T is considered to be a consistent estimator of the population parameter Q. This means that as the sample size increases, the estimator T will provide more accurate estimates of the true population parameter.
Therefore, the correct answer is option 'C' which states that both the expectation of T being equal to Q and the variance of T approaching zero as the sample size increases are necessary conditions for T to be a consistent estimator.
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The statistic T is said to be a consistent estimator of the population parameter Q ifa)E(T) = Qb)V(T) ⇒ o as n → ∞c)Both (A) and (B)d)None of the aboveCorrect answer is option 'C'. Can you explain this answer?
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