Point estimation is a statistical technique used to provide a single value as an estimate of an unknown population parameter, such as the mean, variance, or proportion. This value is calculated from sample data and serves as the best guess or approximation of the true parameter.

Key Concepts in Point Estimation:

1. Estimator: A rule or formula used to compute the estimate from the sample data. For example:

   • Sample mean ($\bar{x}$) is an estimator of the population mean ($\mu$).
   • Sample proportion ($\hat{p}$) is an estimator of the population proportion ($p$).

2. Estimate: The actual numerical value obtained from the estimator after applying it to the data.

3. Properties of a Good Estimator:

   • Unbiasedness: The expected value of the estimator equals the true parameter ($E[\hat{\theta}] = \theta$).
   • Consistency: As the sample size increases, the estimator converges to the true parameter value.
   • Efficiency: Among all unbiased estimators, the one with the smallest variance is considered efficient.
   • Sufficiency: An estimator is sufficient if it captures all relevant information in the data about the parameter.

4. Examples of Point Estimators:

   • Sample mean ($\bar{x}$) for the population mean ($\mu$).
   • Sample variance ($s^2$) for the population variance ($\sigma^2$).
   • Maximum likelihood estimator (MLE), which maximizes the likelihood of observing the given sample.

5. Comparison to Interval Estimation: While point estimation gives a single value, interval estimation provides a range of values (confidence intervals) that likely contain the parameter.

---

Would you like an example or deeper explanation?

Related Questions:

1. What are common methods to calculate point estimators like MLE?
2. How does point estimation differ from hypothesis testing?
3. Can you explain the bias-variance tradeoff in point estimation?
4. What are the limitations of using point estimates?
5. How is point estimation used in real-world scenarios?

Tip:

Always pair point estimates with confidence intervals or measures of variability to understand the reliability of the estimate.