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Complete Estimator

  • An estimator that yields unbiased estimates of a population parameter (no systematic bias).
  • It repeatedly produces estimates equal to the true population value in expectation.
  • Common examples from the source are the sample mean and the sample median.

A complete estimator is a statistical method that provides an unbiased estimate of a population parameter. That is, the estimator consistently produces estimates that are equal to the true population value, without any systematic bias.

Being unbiased means the estimator’s expected value equals the true value of the population parameter. A complete estimator, as described in the source, is therefore a reliable and accurate tool for estimating population characteristics because it does not systematically over- or under-estimate the parameter.

The sample mean estimates the population mean by summing all observations in a sample and dividing by the sample size. For a sample of 10 people with ages 25, 30, 35, 40, 45, 50, 55, 60, 65, and 70:

Sample mean=25+30+35+40+45+50+55+60+65+7010=47510=47.5\text{Sample mean} = \frac{25 + 30 + 35 + 40 + 45 + 50 + 55 + 60 + 65 + 70}{10} = \frac{475}{10} = 47.5

This sample mean is an unbiased estimate of the population mean, because it is calculated using all observations in the sample and it consistently produces estimates that are equal to the true population value.

The sample median estimates the population median by arranging observations in numerical order and selecting the middle observation. For the same sample of 10 ages given above, the source presents the median calculation as:

Sample median=35+402=752=37.5\text{Sample median} = \frac{35 + 40}{2} = \frac{75}{2} = 37.5

According to the source, this sample median is an unbiased estimate of the population median, because it is calculated using the middle observation in the sample and it consistently produces estimates that are equal to the true population value.