Estimation

Abstract

Assume a given population with distribution function F(x). In general, the distribution and its characteristics or parameters are not known. Suppose we are interested in say the expectation μ and the variance $\sigma ^{2}$. (Alternatively, if the data are binary, we may be interested in the population proportion π). As outlined previously, we can learn about the population or equivalently its distribution function F, through (random) sampling. The data may then be used to infer properties of the population, hence the term indirect inference. At the outset, it is important to emphasize that the conclusions drawn may be incorrect, particularly if the sample is small, or not representative of the underlying population. The tools of probability may be used to provide measures of the accuracy or correctness of the estimates or conclusions. We will focus on the estimation of unknown parameters or characteristics. Assume $\theta$ to be the object of interest, then we differentiate two types of procedures: point estimation and interval estimation.