The scope of mathematical statistics. The bounds of mathematical statistics are not sharply denned. It is not uncommon to include under mathematical statistics such topics as interpolation theory, approximate integration, periodogram analysis, index numbers, actuarial theory, and various other topics from the calculus of observations. In fact, it seems that mathematical statistics in its most extended meaning may be regarded as including all the mathematics applied to the analysis of quantitative data obtained from observation. On the other hand, a number of mathematicians and statisticians have implied by their writings a limitation of mathematical statistics to the consideration of such questions of frequency, probability, averages, mathematical expectation, and dispersion as are likely to arise in the characterization and analysis of masses of quantitative data. Borel has expressed this somewhat restricted point of view in his statement that the general problem of mathematical statistics is to determine a system of drawings carried out with urns of fixed composition, in such a way that the results of a series of drawings lead, with a very high degree of probability, to a table of values identical with the table of observed values.

On account of the different views concerning the boundaries of the field of mathematical statistics there arose early in the preparation of this monograph questions of some difficulty in the selection of topics to be included.