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Since its introduction in 1972, Stein’s method has offered a completely novel way of evaluating the quality of normal approximations. Through its characterizing equation approach, it is able to provide approximation error bounds in a wide variety of situations, even in the presence of complicated dependence. Use of the method thus opens the door to the analysis of random phenomena arising in areas including statistics, physics, and molecular biology. Though Stein's method for normal approximation is now mature, the literature has so far lacked a complete self contained treatment. This volume contains thorough coverage of the method’s fundamentals, includes a large number of recent developments in both theory and applications, and will help accelerate the appreciation, understanding, and use of Stein's method by providing the reader with the tools needed to apply it in new situations. It addresses researchers as well as graduate students in Probability, Statistics and Combinatorics.

Approximation theory. --- Distribution (Probability theory). --- Electronic books. -- local. --- Mathematics --- Physical Sciences & Mathematics --- Mathematical Statistics --- Algebra --- Distribution (Probability theory) --- Theory of approximation --- Distribution functions --- Frequency distribution --- Mathematics. --- Probabilities. --- Probability Theory and Stochastic Processes. --- Functional analysis --- Functions --- Polynomials --- Chebyshev systems --- Characteristic functions --- Probabilities --- Distribution (Probability theory. --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk

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Self-normalized processes are of common occurrence in probabilistic and statistical studies. A prototypical example is Student's t-statistic introduced in 1908 by Gosset, whose portrait is on the front cover. Due to the highly non-linear nature of these processes, the theory experienced a long period of slow development. In recent years there have been a number of important advances in the theory and applications of self-normalized processes. Some of these developments are closely linked to the study of central limit theorems, which imply that self-normalized processes are approximate pivots for statistical inference. The present volume covers recent developments in the area, including self-normalized large and moderate deviations, and laws of the iterated logarithms for self-normalized martingales. This is the first book that systematically treats the theory and applications of self-normalization.

Grenzwertsatz. --- Limit theorems (Probability theory). --- Mathematical statistics. --- t-test (Statistics). --- Limit theorems (Probability theory) --- Mathematical statistics --- t-test (Statistics) --- Mathematics --- Physical Sciences & Mathematics --- Mathematical Statistics --- Probabilities. --- Statistical inference --- Statistics, Mathematical --- Probability --- Statistical methods --- Mathematics. --- Statistics. --- Probability Theory and Stochastic Processes. --- Statistical Theory and Methods. --- Combinations --- Chance --- Least squares --- Risk --- Statistics --- Probabilities --- Sampling (Statistics) --- Distribution (Probability theory. --- Distribution functions --- Frequency distribution --- Characteristic functions --- Statistics . --- Statistical analysis --- Statistical data --- Statistical science --- Econometrics

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Self-normalized processes are of common occurrence in probabilistic and statistical studies. A prototypical example is Student's t-statistic introduced in 1908 by Gosset, whose portrait is on the front cover. Due to the highly non-linear nature of these processes, the theory experienced a long period of slow development. In recent years there have been a number of important advances in the theory and applications of self-normalized processes. Some of these developments are closely linked to the study of central limit theorems, which imply that self-normalized processes are approximate pivots for statistical inference. The present volume covers recent developments in the area, including self-normalized large and moderate deviations, and laws of the iterated logarithms for self-normalized martingales. This is the first book that systematically treats the theory and applications of self-normalization.

Statistical science --- Operational research. Game theory --- stochastische analyse --- kansrekening --- statistisch onderzoek