Outline of a Theory of Statistical Estimation Based on the Classical Theory of Probability

TLDR

Estimation problems involve both practical and theoretical aspects, with the practical side focusing on populations that cannot be exhaustively studied. The study aims to distinguish these practical and theoretical aspects of estimation and illustrate this with the example of approximating a population mean. The authors propose using samples from the population to estimate constants such as the population mean.

Abstract

We shall distinguish two aspects of the problems of estimation . (i) the practical and (ii) the theoretical. The practical aspect may be described as follows: (i a ) The statistician is concerned with a population, π, which for some reason or other cannot be studied exhaustively. It is only possible to draw a sample from this population which may be studied in detail and used to form an opinion the values of certain constants describing the properties of the population π. For example, it may be desired to calculate approximately the mean of a certain character possessed by the individuals forming the population π, etc.