What is a Point Estimate?
Watch the video for an overview and example, or read on below:
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).
In more formal terms, the estimate occurs as a result of point estimation applied to a set of sample data. Points are single values, in comparison to interval estimates, which are a range of values. For example, a confidence interval is one example of an interval estimate.
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.
- 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”. More info.
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“Klein, G. (2013). The Cartoon Introduction to Statistics. Hill & Wamg.”