Selected PapersSpringer, 6 de des. 2012 - 518 pàgines Herbert Robbins is widely recognized as one of the most creative and original mathematical statisticians of our time. The purpose of this book is to reprint, on the occasion of his seventieth birthday, some of his most outstanding research. In making selections for reprinting we have tried to keep in mind three potential audiences: (1) the historian who would like to know Robbins' seminal role in stimulating a substantial proportion of current research in mathematical statistics; (2) the novice who would like a readable, conceptu ally oriented introduction to these subjects; and (3) the expert who would like to have useful reference material in a single collection. In many cases the needs of the first two groups can be met simulta neously. A distinguishing feature of Robbins' research is its daring original ity, which literally creates new specialties for subsequent generations of statisticians to explore. Often these seminal papers are also models of exposition serving to introduce the reader, in the simplest possible context, to ideas that are important for contemporary research in the field. An example is the paper of Robbins and Monro which initiated the subject of stochastic approximation. We have also attempted to provide some useful guidance to the literature in various subjects by supplying additional references, particularly to books and survey articles, with some remarks about important developments in these areas. |
Continguts
Empirical Bayes Methodology and Compound Decision Theory | 1 |
103 Prediction and Estimation for the Compound Poisson Distribution | 70 |
124 Some Thoughts on Empirical Bayes Estimation | 87 |
Sequential Experimentation and Analysis | 99 |
107 Adaptive Design in Regression and Control with T L Lai | 136 |
129 Optimal Sequential Sampling From Two Populations with T L Lai | 182 |
Sequential Estimation and Testing | 197 |
64 On the Asymptotic Theory of FixedWidth Sequential Confidence | 211 |
70 Iterated Logarithm Inequalities with D A Darling | 254 |
83 Boundary Crossing Probabilities for the Wiener Process and Sample | 271 |
91 A Class of Stopping Rules for Testing Parametric Hypotheses with | 293 |
Probability and Inference | 327 |
W Hoeffding | 349 |
21 Application of the Method of Mixtures to Quadratic Forms in Normal | 358 |
27 Minimum Variance Estimation Without Regularity Assumptions with | 367 |
Measure with T E Harris | 396 |
68 Finding the Size of a Finite Population with D A Darling | 218 |
51 A Bayes Test of p Versus p with S Moriguti | 225 |
116 Sequential Medical Trials with T L Lai B Levin and D Siegmund | 247 |
Fair Games with Y S Chow | 406 |
102 Maximally Dependent Random Variables with T L Lai | 506 |
Altres edicions - Mostra-ho tot
Frases i termes més freqüents
Acad applications assume assumption asymptotic asymptotically optimal b₁ Bayes estimator compute convergence Corollary decision function decision problem decision rule defined denote dF(y dG(X distribution function equation estimate example exists expected finite fixed follows given H₁ Hence HERBERT ROBBINS holds independent random variables inequality integer interval iterated logarithm large numbers law of large Lemma lim inf linear log log martingale Math Mathematical Statistics measure method minimax minimizing Natl normal distribution observations obtain optimal stopping parameter population positive constants probability Proc proof of Theorem prove regression risk function sampling rule satisfies Section sequence sequential Siegmund solution statistical decision stochastic approximation stochastic approximation scheme stopping rule Suppose t₁ theory toss unknown variance Wiener process x₁ Xn+1 y₁