Point Estimate in Statistics

What is a Point Estimate

In simple terms, any statistic can be a point estimate. A statistic is an estimator of some parameter in a population. For example:

• The sample standard deviation (s) is a point estimate of the population standard deviation (σ).
• The sample mean (̄x) is a point estimate of the population mean, μ
• The sample variance (s² is a point estimate of the population variance (σ²)

Finding the Estimates

Four of the most common ways to find an estimate:

• The Method of Moments: is based on the law of large numbers and uses relatively simple equations to find point estimates. Is often not too accurate and has a tendency to be biased. More info.
• Maximum Likelihood: uses a model (for example, the normal distribution) and uses the values in the model to maximize a likelihood function. This results in the most likely parameter for the inputs selected. More info.
• Bayes Estimators: minimize the average risk (an expectation of random variables). More info.
• Best Unbiased Estimators: several unbiased estimators can be used to approximate a parameter. Which one is “best” depends on what parameter you are trying to find. For example, with variance, the estimator with the smallest variance is “best”