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Interval Estimation

Interval estimation is the measurement and analysis of statistical parameters such as the mean of a population. It calculates the range of values or an interval where the parameter is estimated to be located. When choosing an interval, the parameter falls within a 95% or 99% probability. This probability is known as the confidence coefficient. It is for this reason that intervals are known as confidence intervals. The upper and lower confidence limits are the endpoints of the confidence intervals.

Rao-Blackwell Theorem

It is also known as the Rao-Blackwellization or the Rao-Blackwell-Kolmogorov theorem. This theorem provides an effective way of improving the efficiency of initial estimators. We are assuming that you already know that estimators are random variables that can be observed and used to measure quantities. For example, a population means can be estimated using an observable sample mean.

Method of Moments

The method of moments is a technique used to predict and measure the parameters of a population like the mean and standard deviation. It involves using known facts about a given population and extending your ideas to your sample. Method of moments is preferred to other methods like maximum likelihood because it is simple and can be performed by hand. However, it may also provide inaccurate parameter estimates. Also, the method of moments may not give you sufficient statistics.