Statistics of nonnumeric data in forty years (review)
Alexander Ivanovich Orlov · Industrial laboratory Diagnostics of materials · 2019
Forty years ago, the statistics of nonnumeric data was singled out into an independent area of mathematical research methods. First the term «statistics of objects of nonnumeric nature» was used. The textbook on nonnumeric statistics is entitled «Nonnumeric Statistics». Statistics of nonnumeric data is one of the four main fields of applied statistics (along with the statistics of numbers, multivariate statistical analysis, statistics of time series and random processes). Statistics of nonnumeric data is divided into statistics in spaces of general nature and sections devoted to specific types of nonnumeric data (statistics of interval data, statistics of fuzzy sets, statistics of binary relations, etc.). Currently, statistics in spaces of general nature is the central part of applied statistics, and the statistics of nonnumeric data that includes it is the main area of applied statistics. This statement is confirmed by analysis of publications in the section «Mathematical Methods of Research» of our journal. This article is devoted to analysis of the main ideas of statistics of nonnumeric data against the background of the development of applied statistics on the basis of the new paradigm of the methods of mathematical research. Different types of nonnumeric data are considered along with the history of development of the statistics of nonnumeric data and statistical science. The basic ideas of statistics in spaces of general nature are analyzed: mean values, laws of large numbers, extreme statistical problems, nonparametric estimators of the probability distribution density, classification methods (diagnostics and cluster analysis), and statistics of the integral type. Some statistical methods for data analysis in specific nonnumeric spaces are briefly discussed: nonparametric statistics (in most cases, real distributions significantly differ from normal), statistics of fuzzy sets, expert estimation theory (Kemeny median as a sample average of expert orderings), etc. Some unsolved problems in statistics on nonnumeric data are also discussed.