Question

A good estimator should be _______.

• A. Consistent
• B. Sufficient
• C. Efficient
• D. All of the above

Hint:

A good estimator must be consistent, efficient, and sufficient to be effective in statistical analysis.

Answer 1

The Correct Option is D

A good estimator should have the following properties: - **Consistency**: The estimator converges to the true value as the sample size increases. - **Sufficiency**: The estimator makes use of all available data without discarding useful information. - **Efficiency**: The estimator has the smallest variance among all unbiased estimators.
Step 2: Analyzing the options.

• (A) Consistent: Correct. Consistency ensures that the estimator converges to the true parameter value as the sample size increases.
• (B) Sufficient: Correct. A sufficient estimator uses all available information and does not lose relevant data.
• (C) Efficient: Correct. Efficiency refers to the estimator having the least variance among unbiased estimators.
• (D) All of the above: Correct. A good estimator should possess consistency, sufficiency, and efficiency.

Step 3: Conclusion.
The correct answer is (D) All of the above, as all these properties define a good estimator. Final Answer:} All of the above.