Herbert Robbins Selected Papers

Front Matter....Pages i-xli
Front Matter....Pages 1-5
Asymptotically Subminimax Solutions of Compound Statistical Decision Problems....Pages 7-24
Asymptotic Solutions of the Compound Decision Problem for Two Completely Specified Distributions....Pages 25-39
An Empirical Bayes Approach to Statistics....Pages 41-47
The Empirical Bayes Approach to Statistical Decision Problems....Pages 49-68
Prediction and estimation for the compound Poisson distribution....Pages 70-71
An empirical Bayes estimation problem....Pages 72-73
Estimating Many Variances....Pages 75-85
Jerzy Neyman Memorial Lecture Some Thoughts on Empirical Bayes Estimation....Pages 87-97
Front Matter....Pages 99-101
A Stochastic Approximation Method....Pages 102-109
A Convergence Theorem for Non Negative Almost Supermartingales and Some Applications....Pages 111-135
Adaptive design in regression and control....Pages 136-137
Adaptive Design and Stochastic Approximation....Pages 138-163
Some Aspects of the Sequential Design of Experiments....Pages 169-177
A Sequential Decision Problem with a Finite Memory....Pages 178-181
Optimal sequential sampling from two populations....Pages 182-184
Reducing the Number of Inferior Treatments in Clinical Trials....Pages 185-186
Sequential Tests Involving Two Populations....Pages 188-195
Sequential Estimation of the Mean of a Normal Population....Pages 199-209
On the Asymptotic Theory of Fixed-Width Sequential Confidence Intervals for the Mean....Pages 211-216
Finding the Size of a Finite Population....Pages 218-224
Front Matter....Pages 99-101
A Bayes Test of “p≤½” versus “p≤½”....Pages 225-246
Sequential medical trials....Pages 247-250
Iterated Logarithm Inequalities....Pages 254-258
Statistical Methods Related to the Law of the Iterated Logarithm....Pages 259-271
Boundary Crossing Probabilities for the Wiener Process and Sample Sums....Pages 272-291
A Class of Stopping Rules for Testing Parametric Hypotheses....Pages 293-297
Statistical Tests of Power One and the Integral Representation of Solutions of Certain Partial Differential Equations....Pages 299-326
Front Matter....Pages 327-330
On the Measure of a Random Set....Pages 332-336
Complete Convergence and the Law of Large Numbers....Pages 337-348
The Central Limit Theorem for Dependent Random Variables....Pages 349-356
Application of the Method of Mixtures to Quadratic Forms in Normal Variates....Pages 358-366
Minimum Variance Estimation without Regularity Assumptions....Pages 367-372
Ergodic Property of the Brownian Motion Process....Pages 373-381
On The Equidistribution of Sums of Independent Random Variables....Pages 382-395
Ergodic Theory of Markov Chains Admitting an Infinite Invariant Measure....Pages 396-400
A Remark on Stirling’s Formula....Pages 402-405
On Sums of Independent Random Variables with Infinite Moments and “Fair” Games....Pages 406-411
A Martingale System Theorem and Applications....Pages 413-424
On Optimal Stopping Rules....Pages 425-441
Optimal Selection Based on Relative Rank....Pages 443-452
Front Matter....Pages 327-330
Optimal Stopping....Pages 453-463
Moments of Randomly Stopped Sums....Pages 465-475
On the „Parking“ Problem....Pages 477-493
Estimating the Total Probability of the Unobserved Outcomes of an Experiment....Pages 494-495
Mathematical Probability in Election Challenges....Pages 497-504
Maximally dependent random variables....Pages 506-508
Strong consistency of least squares estimates in multiple regression....Pages 510-512
A Note on the ‘Under adjustment Phenomenon’....Pages 513-515
Back Matter....Pages 517-518