Home › MCQs › SSC Statistics › Question #1987
Back to Questions
SSC Statistics QUESTION #1987
Question 1
A point estimator \(\hat{\theta}\) is said to be consistent if:
  • \(E(\hat{\theta}) = \theta\) for all sample sizes
  • Its variance is smaller than all other unbiased estimators
  • \(\hat{\theta} \xrightarrow{p} \theta\) as \(n \to \infty\)✔️
  • Its mean squared error equals zero
Correct Answer Explanation
Consistency means the estimator converges in probability to the true parameter as sample size increases: \(\lim_{n\to\infty} P(|\hat{\theta} - \theta| > \varepsilon) = 0\) for any \(\varepsilon > 0\). This is a large-sample (asymptotic) property, unlike unbiasedness which is a finite-sample property.