Parameter Estimation

Parameter estimation is crucial in statistical decision making. It is common practice in civil engineering to collect sample data to estimate the parameters of population distribution.  The parameters estimated from the sample data and their sampling distributions are useful in estimating the population parameters. Two types of estimates are possible from the sample data, namely, point estimates, interval estimates.

Properties of the estimators

An estimator is the rule or the method of estimation and an estimate is the value the estimator yields in a particular case. There may be several estimators but an appropriate estimator must have the following properties.

1. Unbiasedness
2. Consistency
3. Minimum Variability
4. Efficiency
5. Sufficiency

When the expectation of the unbiased estimator yields the corresponding population parameter then the estimator is known as unbiased estimator. The difference between the expectation of the unbiased estimator and the corresponding population parameter is known as bias.

For example is the sample mean and if is to be the unbiased estimator for the population mean µ must be equal to μ. In this case the estimate for the population mean is .

The estimator must also have minimum variance when it is obtained through repeated sampling. A sufficient estimator provides as much information as possible on the sample data and better than any other estimator.

Point Estimators

X₁, X₂, X₃, …. X_n is a random sample of size n collected from the population with parameters µ and σ². The sample has mean and variance S². In this case the unbiased point estimators for the population parameters are and . Point estimates may lead to errors when the variance associated to the estimators is high. To avoid this, confidence intervals can be provided for the population parameters with the help of the sampling distributions.