Interval Estimator

Definition

An interval estimator is a type of estimator that provides a range of values within which a population parameter is expected to lie, along with a specified level of confidence. This is crucial because it not only estimates the parameter but also indicates the uncertainty associated with that estimate. Interval estimators often take the form of confidence intervals and are characterized by their properties like reliability and accuracy, influencing their admissibility and completeness.

5 Must Know Facts For Your Next Test

1. Interval estimators are often constructed using sample statistics like the sample mean and standard deviation to create a range around an estimate.
2. A common type of interval estimator is the confidence interval, which provides a range based on a specified confidence level.
3. The width of an interval estimator is influenced by factors such as sample size, variability in the data, and the desired confidence level.
4. Interval estimators can be evaluated for their properties, such as whether they are unbiased or how consistent they are across different samples.
5. Admissibility relates to whether an interval estimator is the best option among competing estimators in terms of minimizing expected loss.

Review Questions

• How do interval estimators provide more information than point estimators in statistical analysis?
  • Interval estimators offer a range of values, reflecting the uncertainty and variability inherent in estimating population parameters, unlike point estimators that provide only a single value. By indicating where the true parameter may lie with a certain level of confidence, interval estimators help researchers understand potential errors in their estimates. This added context is essential for making informed decisions based on statistical analysis.
• What role do properties such as bias and consistency play in evaluating interval estimators for their effectiveness?
  • When evaluating interval estimators, properties like bias and consistency are crucial for determining their reliability. A biased estimator will systematically misestimate parameters, while consistency ensures that as sample size increases, the estimator converges to the true parameter value. By understanding these properties, statisticians can choose more effective interval estimators that provide accurate information about population parameters.
• Evaluate how the concepts of admissibility and completeness apply to interval estimators in decision-making contexts.
  • Admissibility and completeness are important concepts when considering which interval estimator to use in decision-making processes. An admissible interval estimator cannot be improved upon without increasing expected loss, making it a strong candidate for practical use. Completeness ensures that all relevant information about the parameter is captured within the estimator. Together, these concepts guide statisticians to select interval estimators that not only provide reliable estimates but also minimize potential risks associated with decision-making.

Related terms

Point Estimator: A point estimator is a single value or point that serves as an estimate of a population parameter, providing no information about the variability or uncertainty of the estimate.

Confidence Level: The confidence level is the probability that the interval estimator will contain the true population parameter, commonly expressed as a percentage like 95% or 99%.

Bias: Bias refers to the systematic error in an estimator, which can cause it to consistently overestimate or underestimate the true population parameter.