Point Estimation

If I have a known distribution, but I don't know what the parameter values (e.g., , , etc.) are, how can I estimate these population parameters using a sample of size n (sample statistics)? Given a population parameter of interest, e.g., the population mean or the population proportion , we want to use a sample to compute a number that represents a ``good'' guess for the true value of the parameter. This number is called a point estimate. We will use the Greek letter (``theta'') to represent any of the parameters we will study such as , , , etc.

• Estimate A point estimate/ of a parameter is a single number based on the sample data that we can consider to be the most plausible value of .
• Estimator The statistic (formula) used to obtain the point estimate.

To emphasize:

• • Point Estimator = Statistic (formula)
  • Point Estimate = Number (calculated value)

• Point Estimators for Different Situations
• Properties of Point Estimators
• Minimum Variance Unbiased Estimation