Издательство Birkhäuser, 2001, -366 pp.This handbook deals with the oldest problem in stochastics and goes back to its deepest roots in order to elaborate on the old problem from a different point of view, thus addressing professional and academic statisticians. New solutions for the old problem are obtained and subsequently presented for the user without assuming mathematical skills and a deep knowledge of statistics. The aim is to offer statistical methods to the potential user in a comparable way as sophisticated technical devices are made available, which can be used by any layman without understanding the underlying physical or chemical principles.
There were two primary motives for writing this handbook. The first one resulted from a consulting project in the course of which proportions had to be estimated. We noticed that the recommended methods are difficult to handle for practitioners and, moreover, they are inaccurate and yield often useless results. This made us think about the "quality" of statistical procedures, and we noticed that the many different criteria used in statistics for assessing the quality of statistical methods have, at most, an auxiliary character. Therefore, we started to look for a way to improve the existing methods, to develop a possibility for evaluating the quality of statistical procedures, and to make their understanding and application easier.
Particularly valuable were Jerzy Neyman's papers on estimation theory, which showed us the direction in which to proceed. By rigorously furthering Neyman's ideas, we finally arrived at something that could be called a geometric approach to statistics or a small sample theory in statistics. This was possible by abandoning the unrealistic assumption of a maximum parameter space and adopting the more realistic aim of developing procedures for appropriately selected bounded parameter ranges. Throughout the handbook, the problems are investigated not asymptotically, but realistically. The approach should be valid for small sample sizes n, as are common in many natural sciences and technology. This primary requirement led to problems and questions that are completely different from the investigation of limits and convergence rates. Thus, the handbook represents a first step toward developing statistics as a (natural) science, and further steps must follow.
The handbook illustrates the approach by applying it to the binomial distribution. Scientists and engineers may benefit in several ways:
- The handbook uses an easy-to-understand terminology, which attempts to reflect the meaning of the relevant concepts in order to avoid ambiguity.
- The proposed methods have a better quality, particularly for small—and medium—size samples.
- There are printed tables for a preliminary analysis of data, and there are tables on a CD-ROM for a more detailed analysis with a so far unrealized size.
Statisticians may benefit by the novel approach, which can be applied to any given situation modeled by random variables and aiming to solve a problem related to prediction, estimation, exclusion, and comparison.
According to its aims, the book is organized in the following way After an introduction into the problem and the state of the art, a unified approach for "estimation and test" theory is developed based on the "measurement & prediction space," which constitutes the basic quantity of the entire theory. The second part of the book is primarily directed at statisticians with a sound background in mathematics. The new approach and the resulting methods are explained in detail and illustrated by examples.Introduction
Stochastics
Models Related to the Probability of an Event
Traditional Estimation Procedures
Theory
Measurement and Prediction Procedures
Complete Measurement Procedures
Exclusion Procedures
Comparison Procedures
Introduction to the Tables
Measurement Intervals
Prediction Regions
Application
Measuring a Probability
Excluding a Probability
Comparing Probabilities
Tables
